Fernandez Bonder, Julian
Researcher
Telephone: 5285-9829
Email Address: jfbonder@dm.uba.ar
Job: Researcher
Office: 2614
Web: http://mate.dm.uba.ar/~jfbonder/index.html
Areas
Research Areas:
Differential equations

CV

1/ Personal data

Name: Julián Fernández Bonder

Birth date: 05 August 1969

Professional address (with telephone and e-mail): 

Math Department, Universidad de Buenos Aires and 

Instituto de Cálculo, CONICET. 

Intendente Güiraldes 2160, Ciudad Universitaria, 0+infinity Building, 

Buenos Aires, ARGENTINA. 

+54 11 5285 9829

 

2/ Highest obtained degree (with indication of place and date)

PhD in Mathematics, Universidad de Buenos Aires, 2002.

 

3/ Current position

Full Professor, Math Department, Universidad de Buenos Aires and

Principal Researcher at CONICET.

 

4/ Other duties/ positions

Academic Secretary, School of Natural and Exact Sciences, Universidad de Buenos Aires. 2022-2026.

 

5/ Awards, fellowships and external recognition

Misha-Cotlar award to young mathematician in Argentina by the National Academy of Exact and Natural Sciences, 2009.

 

6/ Ongoing funded research projects with dates, titles, sources of funding

  • PICT 2016-1022 from National Agency for the Promotion of Science and Technology. 
  • Universidad de Buenos Aires UBACYT Prog. 2018 20020170100445BA.
  • CONICET PIP Nº 11220150100032CO.

Publications

Papers in Scientific Journals

Submitted for Publications:

  1. S. Bahrouni, J. Fernández Bonder, I. Ceresa-Dussel and O. Miyagaki. Peridynamics and anisotropic fractional Sobolev spaces with variable exponents. pdf
  2. J. Fernández Bonder and A.M. Salort. On the first eigenvalue of the generalized laplacian. pdf
  3. C. De Vita, J. Fernández Bonder and P. Groisman. The energy landscape of the Kuramoto model in one-dimensional random geometric graphs with a hole. pdf
  4. J. Fernández Bonder and J.F. Spedaletti. Ljusternik--Schnirelmann eigenvalues for the fractional $m-$Laplacian without the $\Delta_2$ condition. pdf
  5. I. Ceresa Dussel, J. Fernández Bonder and A. Silva. A priori estimates for solutions of $g-$Laplace type problems pdf
  6. J. Fernández Bonder and A.M. Salort. Asymptotic behavior for anisotropic fractional energies. pdf

In Press:

  1. J. Fernández Bonder and A. Silva. The concentration-compactness principle for Orlicz spaces and applications. To appear in Math. Nach. pdf
  2. I. Ceresa Dussel and J. Fernández Bonder. Existence of Eigenvalues for Anisotropic and Fractional Anisotropic Problems via Ljusternik-Schnirelmann Theory. To appear in Topol Methods Nonlinear Anal. pdf
  3. J. Fernández Bonder, A.M. Salort and H. Vivas. Homogeneous eigenvalue problems in Orlicz-Sobolev spaces To appear in Topol. Methods Nonlinear Anal. pdf

Published:

  1. A. Aragón, J. Fernández Bonder and D. Rubio. Effective numerical computations of p(x)--Laplace equations in 2D. Int. J. Comput. Math. 100 (2023), no. 11, 2111--2123. pdf
  2. J. Fernández Bonder, A.M. Salort and H. Vivas. Global Hölder regularity for eigenfunctions of the fractional g-Laplacian. J. Math. Appl. Anal. 526 (2023), no. 1, Paper No. 127332, 15 pp. pdf
  3. I. Ceresa Dussel and J. Fernández Bonder. A Bourgain-Brezis-Mironescu formula for anisotropic fractional Sobolev spaces and applications to anisotropic fractional differential equations J. Math. Anal. Appl., 519 (2023), no. 2, Paper 126805, 25pp. pdf
  4. J. Fernández Bonder, A.M. Salort and H. Vivas. Interior and up to the boundary regularity for the fractional $g-$Laplacian: the convex case. Nonlinear Anal., 223 (2022), Paper No. 113060, 31pp.. pdf
  5. J. Fernández Bonder, M. Pérez-Llanos and A. Salort. A Hölder infinity laplacian obtained as limit of Orlicz fractional laplacians.  Rev. Mat. Complut. 35 (2022), no. 2, 447--483. pdf
  6. J. Fernández Bonder, A. Silva and J.F. Spedaletti. Gamma convergence and asymptotic behavior for eigenvalues of nonlocal problems. Discrete and Continuous Dynamical Systems, 41 (2021), no. 5, 2125--2140.  pdf
  7. J. Fernández Bonder, Z. Cheng and H. Mikayelyan. Fractional optimal maximization problem and the unstable fractional obstacle problem. Journal of Mathematical Analysis and Applications, 495 (2021), 124686.  pdf
  8. J. Fernández Bonder and A.M. Salort. Magnetic fractional order Orlicz-Sobolev spaces. Studia Mathematica, 259 (2021), 1--24.   pdf
  9. P. De Nápoli, J. Fernández Bonder and A.M. Salort. A Pólya-Szegó principle for general fractional Orlicz-Sobolev spaces.  Complex Variables and Elliptic Equations, 66 (2021), no. 4, 546--568. pdf
  10. J. Fernández Bonder and A.M. Salort Stability of solutions for nonlocal problems. Nonlinear Analysis, 200 (2020), 112080.   pdf
  11. J. Fernández Bonder, Z. Cheng and H. Mikayelyan. Optimal rearrangement problem and normalized obstacle problem in the fractional setting.  Advances in Nonlinear Analysis, 9 (2020), no. 1, 1592--1606. pdf
  12. J. Fernández Bonder and A.M. Salort. Fractional order Orlicz-Sobolev spaces. J. Functional Anal. 277 (2019), no. 2, 333--367. pdf
  13. J. Fernández Bonder, A. Silva and J.F. Spedaletti. Uniqueness of minimal energy solutions for a semilinear problem involving the fractional laplacian. Proc. Amer. Math. Soc. 147 (2019), no. 7, 2925--2936. pdf
  14. J. Fernández Bonder, A. Ritorto and A.M. Salort. Shape optimization problems for nonlocal operators. Adv. Calc. Var. 11 (2018), no. 4, 373--386. pdf
  15. J. Fernández Bonder, N. Saintier and A. Silva. The concentration-compactness principle for fractional order Sobolev spaces in unbounded domains and applications to the generalized fractional Brezis-Nirenberg problem. NoDEA Nonlinear Differential Equations Appl. 25 (2018), no. 6, Art. 52, 25 pp. pdf
  16. C. Baroncini and J. Fernández Bonder. A shape-derivative approach to some PDE model in image restoration. Electron. J. Differential Equations, Vol. 2018 (2018), No. 146, pp. 1-18.   pdf
  17. J. Fernández Bonder, J.D. Rossi and J.F. Spedaletti. Optimal design problems for the first $p-$fractional eigenvalue with mixed boundary conditions. Adv. Nonlinear Stud. 18 (2018), no. 2, 323--335.  pdf
  18. L. Del Pezzo, J. Fernández Bonder and L. López Ríos.  An optimization problem for the first eigenvalue of the $p-$fractional laplacian. Math. Nachr. 291 (2018), no. 4, 632--651.  pdf
  19. J. Fernández Bonder and J.F. Spedaletti.  Some nonlocal optimal design problems. J. Math. Anal. Appl., 459 (2018), no. 2, 906--931.   pdf
  20. C. Baroncini, J. Fernández Bonder and J.F. Spedaletti. Continuity results with respect to domain perturbation for the fractional $p-$laplacian. Appl. Math. Lett. 75 (2018), 59--67.  pdf
  21. J. Fernández Bonder, A. Ritorto and A.M. Salort. H-convergence result for nonlocal elliptic-type problems via Tartar's method. SIAM J. Math. Anal., 49 (2017), no. 4, 2387--2408.   pdf
  22. J. Fernández Bonder, J.P. Pinasco and A.M. Salort. Homogenization of Fucik eigencurves. Mediterr. J. Math., 14 (2017), no. 2, 14--90. pdf
  23. J. Fernández Bonder and J.F. Spedaletti. A shape optimization problem for Steklov eigenvalues in oscillating domains.   ESAIM Control Optim. Calc. Var. 23 (2017), 373--390. pdf
  24. J.P. Borthagaray, J. Fernández Bonder and A. Silva.  A mass transportation approach for Sobolev inequalities in variable exponent spaces.   Manuscripta Math. 151 (2016), no. 1-2, 133--146. pdf
  25. J. Fernández Bonder, N. Saintier and A. Silva. A Gamma convergence approach to the critical Sobolev embedding in variable exponent spaces.  J. Math. Anal. Appl., 442 (2016), no. 1, 189--205. pdf
  26. J. Fernández Bonder, J.P. Pinasco and A.M. Salort. A Lyapunov type inequality for indefinite weights and eigenvalue homogenization.   Proc. Amer. Math. Soc. 144 (2016), no. 4, 1669--1680. pdf
  27. J. Fernández Bonder, J.P. Pinasco and A.M. Salort. Eigenvalue homogenization for quasilinear elliptic equations with different boundary conditions.  Electron. J. Differential Equations, 2016 (2016), no. 30, 1--15. pdf
  28. J. Fernández Bonder, J.P. Pinasco and A.M. Salort. Eigenvalue homogenization problem with indefinite weights.   Bull. Aust. Math. Soc., 93 (2016), no. 1, 113--127. pdf
  29. C. Baroncini and J. Fernández Bonder. An extension of a Theorem of V. Sverák to variable exponent spaces.  Commun. Pure Appl. Anal.  14 (2015), no. 5, 1987--2007. pdf
  30. J. Fernández Bonder, N. Saintier and A. Silva. Existence of solution to a critical trace equation with variable exponent.  Asymp. Anal.  93 (2015), 161--185. pdf
  31. J. Fernández Bonder, J.P. Pinasco and A.M. Salort. Quasilinear eigenvalues. Rev. Un. Mat. Argentina  56 (2015), no. 1, 1--25.pdf
  32. J. Fernández Bonder, J.P. Pinasco and A.M. Salort. Convergence rate for quasilinear eigenvalue homogenization. J. Math. Anal. Appl.  423 (2015), 1427--1447. pdf
  33. J. Fernández Bonder, N. Saintier and A. Silva. On the Sobolev trace Theorem for variable exponent spaces in the critical range. Ann. Mat. Pura Appl. (4), 193 (2014), 1607--1628. pdf
  34. J. Fernández Bonder, G. Giubergia and F. Mazzone. An optimization problem for nonlinear Steklov eigenvalues with a boundary potential. J. Math. Anal. Appl.  417 (2014), 234--243. pdf
  35. J. Fernández Bonder, N. Saintier and A. Silva. Existence of solution to a critical equation with variable exponent. Ann. Acad. Sci. Fenn. Math.  37 (2012), 579--594. pdf
  36. J. Fernández Bonder, N. Saintier and A. Silva. On the Sobolev embedding theorem for variable exponent spaces in the critical range.  J. Differential Equations 253 (2012), no. 5, 1604--1620. pdf
  37. L. Del Pezzo, J. Fernández Bonder and W. Neves. Optimal boundary holes for the Sobolev trace constant. J. Differential Equations, 251 (2011), no. 8, 2327--2351. pdf
  38. J. Fernández Bonder and A. Silva. The concentration-compactness principle for variable exponent spaces and applications. Electron. J. Differential Equations, 2010 (2010), no. 141, 1--18. pdf
  39. J. Fernández Bonder, J.P. Pinasco and A.M. Salort. Refined asymptotics for eigenvalues on domains of infinite measure. J. Math. Anal. Appl., 371 (2010), no. 1, 41--56. pdf
  40. J. Fernández Bonder and J.P. Pinasco. Precise asymtotic of eigenvalues of resonant quasilinear systems. J. Differential Equations, 249 (2010), 136--150. pdf
  41. L. Del Pezzo and J. Fernández Bonder. An optimization problem for the first weighted eigenvalue problem plus a potential. Proc. Amer. Math. Soc., 138 (2010), no. 10, 3551--3567. pdf
  42. L. Del Pezzo and J. Fernández Bonder. Remarks on an optimization problem for the $p-$Laplacian. Appl. Math. Lett., 23 (2010), 188--192. pdf
  43. J. Fernández Bonder, S. Martínez and N. Wolanski. A free boundary problem for the $p(x)-$Laplacian. Nonlinear Anal. TMA., 72 (2010), 1078--1103. pdf
  44. P. De Nápoli, J. Fernández Bonder and A. Silva. Multiple solutions for the $p-$laplace operator with critical growth. Nonlinear Anal. TMA., 71 (2009), 6283--6289. pdf
  45. J. Fernández Bonder, P. Groisman and J.D. Rossi. Continuity of the explosion time in stochastic differential equations. Stochastic Anal. Appl., 27 (2009), no. 5, 984--999. pdf
  46. J. Fernández Bonder, R. Orive and J.D. Rossi. The best Sobolev trace constant in periodic media for critical and subcritical exponents. Glasgow Math. J., 51 (2009), 619--630. pdf
  47. L. Del Pezzo and J. Fernández Bonder. Some optimization problems for p-Laplacian type equations. Appl. Math. Optim., 59 (2009), 365--381. pdf
  48. J. Fernández Bonder and P. Groisman. Time--space white noise eliminates global solutions in reaction diffusion equations. Physica D, 238 (2009), 209--215. pdf
  49. J. Fernández Bonder, J.D. Rossi and C.B. Shönlieb. The best constant and extremals of the Sobolev embeddings in domains with holes: The L^\infty case. Illinois J. Math., 52 (2008), no. 4, 1111--1121. pdf
  50. J. Fernández Bonder, J.D. Rossi and C.B. Shönlieb. An optimization problem related to the best Sobolev trace constant in thin domains. Commun. Contemp. Math., 10 (2008), no. 5, 1--18. pdf
  51. J. Fernández Bonder and N. Saintier. Estimates for the Sobolev trace constant with critical exponent and applications. Ann. Mat. Pura Appl. (4), 187 (2008), no. 4, 683--704. pdf
  52. J. Fernández Bonder and J.P. Pinasco. Estimates for eigenvalues of quasilinear elliptic systems. Part II. J. Differential Equations, 245 (2008), no. 4, 875--891. pdf
  53. J. Fernández Bonder, R. Orive and J.D. Rossi. The best Sobolev trace constant in domains with holes for critical or subcritical exponents. ANZIAM J., 49 (2007), 213--230. pdf
  54. J. Fernández Bonder, S. Martínez and J.D. Rossi. Existence results for gradient elliptic systems with nonlinear boundary conditions. NoDEA Nonlinear Differential Equations Appl., 14 (2007), no. 1-2, 153--179. pdf
  55. J. Fernández Bonder, R. Orive and J.D. Rossi. The best Sobolev trace constant in a domain with oscillating boundary. Nonlinear Anal. TMA. 67 (2007), 1173--1180. pdf
  56. J. Fernández Bonder, P. Groisman and J.D. Rossi. Optimization of the first Steklov eigenvalue in domains with holes: A shape derivative approach. Ann. Mat. Pura Appl. (4), 186 (2007), no. 2, 341--358. pdf
  57. L. Del Pezzo, J. Fernández Bonder and J.D. Rossi. An optimization problem for the first Steklov eigenvalue of a nonlinear problem. Differential Integral Equations, 19 (2006), no. 9, 1035--1046. pdf
  58. L. Del Pezzo and J. Fernández Bonder. An optimization problem for the first eigenvalue of the p-Laplacian plus a potential. Commun. Pure Appl. Anal. 5 (2006), no. 4, pp. 675--690. pdf
  59. J. Fernández Bonder, J.D. Rossi and N. Wolanski. On the best Sobolev trace constant and extremals in domains with holes. Bull. Sci. Math. 130 (2006), 565--579. pdf
  60. J. Fernández Bonder. Multiple solutions for the p-laplace equation with nonlinear boundary conditions. Electron. J. Differential Equations, 2006 (2006), no. 37, pp. 1-7. pdf
  61. J. Fernández Bonder, S. Martinez and N. Wolanski. An optimization problem with volume constrain for a degenerate quasilinear operator. J. Differential Equations, 227 (2006), no. 1, pp. 80-101. pdf
  62. J. Dávila, J. Fernández Bonder, P. Groisman, J.D. Rossi and M. Sued. Numerical analysis of stochastic differential equations with explosions Stochastic Anal. Appl., 23 (2005), no. 4, 809--825. ps
  63. J. Fernández Bonder, J.D. Rossi and N. Wolanski. Regularity of the free boundary in an optimization problem related to the best Sobolev trace constant. SIAM J. Control Optim., 44 (2005), no. 5, 1614--1635. pdf
  64. J. Fernández Bonder and J.P. Pinasco. Eigenvalues of the p-laplacian in fractal strings with indefinite weights. J. Math. Anal. Appl., 308 (2005), no. 2, 764--774. pdf
  65. J. Fernández Bonder and J.D. Rossi. On the existence of extremals for the Sobolev trace embedding theorem with critical exponent. Bull. London Math. Soc. 37 (2005), no. 1, 119--125. pdf
  66. J. Fernández Bonder. Multiple positive solutions for quasilinear elliptic problems with sign-changing nonlinearities. Abstr. Appl. Anal. 2004 (2004), no. 12, 1047--1056. pdf
  67. J. Fernández Bonder, S. Martínez and J.D. Rossi. The behavior of the best Sobolev trace constant and extremals in thin domains. J. Differential Equations, 198 (2004), no. 1, 129--148. pdf
  68. J. Fernández Bonder, E. Lami Dozo and J.D. Rossi. Symmetry properties for the extremals of the Sobolev trace embedding. Ann. Inst. H. Poincaré Anal. Non Linéaire. 21 (2004), no. 6, 795--805. pdf
  69. J. Fernández Bonder and N. Wolanski. Uniqueness of limit solutions to a free boundary problem from combustion. SIAM J. Math. Anal., 36 (2004), no. 1, 172--185. pdf
  70. J. Fernández Bonder, R. Ferreira and J.D. Rossi. Uniform bounds for the best Sobolev trace constant. Advanced Nonlinear Studies, 3 (2003), 181--192. pdf
  71. J. Fernández Bonder and J.P. Pinasco. Asymptotic behavior of the eigenvalues of the one dimensional weighted p-laplace operator. Ark. Mat., 41 (2003), 267--280. pdf
  72. G. Acosta, J. Fernández Bonder, P. Groisman and J.D. Rossi. Simultaneous vs. non-simultaneous blow-up in numerical approximations of a parabolic system with nonlinear boundary conditions. M2AN Math. Model. Numer. Anal., 36 (2002), no. 1, 55--68. pdf
  73. G. Acosta, J. Fernández Bonder, P. Groisman and J.D. Rossi. Numerical approximation of a parabolic problem with a nonlinear boundary condition in several space dimensions. Discrete Contin. Dynam. Systems - Series B, 2 (2002), no. 2, 279--294. pdf
  74. J. Fernández Bonder and J.D. Rossi. Asymptotic behavior of the best Sobolev trace constant in expanding and contracting domains. Commun. Pure Appl. Anal. 1 (2002), no. 3, 359--378. pdf
  75. J. Fernández Bonder and J.D. Rossi. A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding. Publ. Mat., 46 (2002), 221--235. pdf
  76. J. Fernández Bonder, P. Groisman and J. D. Rossi. On numerical blow-up sets. Proc. Amer. Math. Soc., 130 (2002), no. 7, 2049--2055. pdf
  77. J. Fernández Bonder and J.D. Rossi. A fourth order elliptic equation with nonlinear boundary conditions. Nonlinear Anal. TMA. 49 (2002), no. 8, 1037--1047. pdf
  78. J. Fernández Bonder and J.D. Rossi. Existence results for the p-Laplacian with nonlinear boundary conditions. J. Math. Anal. Appl., 263 (2001), 195--223. pdf
  79. J. Fernández Bonder and J.D. Rossi. Life span for solutions of the heat equations with a nonlinear boundary condition. Tsukuba J. Math, 25 (2001), no. 1, 215--220. pdf
  80. J. Fernández Bonder and J.D. Rossi. Existence for an elliptic system with nonlinear boundary conditions via fixed point methods. Advances Differential Equations, 6 (2001), no. 1, 1--20. pdf
  81. J. Fernández Bonder and J.D. Rossi. Blow-up vs. spurious steady solutions. Proc. Amer. Math. Soc., 129 (2001), no. 1, 139--144. pdf
  82. G. Acosta, J. Fernández Bonder and J.D. Rossi. Stable manifold approximation for the heat equation with nonlinear boundary conditions. J. Dynam. Differential Equations, 12 (2000), no. 3, 557--578. pdf
  83. J. Fernández Bonder and J.D. Rossi. Asymptotic behavior for a parabolic system with nonlinear boundary conditions. Collect. Math., 51 (2000), no. 3, 285--308. pdf
  84. J. Fernández Bonder and N. Wolanski. A free boundary problem in combustion theory. Interfaces Free Bound., 2 (2000), 381--411. pdf
  85. J. Fernández Bonder, J. P. Pinasco and J.D. Rossi. Existence results for a Hamiltonian elliptic system with nonlinear boundary conditions. Electron. J. Differential Equations, 40 (1999), 1--15. pdf

Proceedings

  1. J. Fernández Bonder, J.P. Pinasco and J.D. Rossi. Infinitely many solutions for an elliptic system with nonlinear boundary conditions. Electron. J. Differential Equations, Conf. 06 (2001), 141--154. pdf
  2. J. Fernández Bonder. On the existence of extremals for the critical Sobolev immersion with variable exponents. Actas del XIII Congreso ''Dr. Antonio A. R. Monteiro'' (2013), 2014, 77--82. pdf

Lecture Notes

  1. J. Fernández Bonder. Ecuaciones Diferenciales Parciales. Lecture notes for the regular course at the University of Buenos Aires, Cursos de Grado del Departamento de Matemática, Fascículo 7, 2015 (in spanish). pdf (1.2Mb)
  2. J. Fernández Bonder and P. Groisman. Explosiones en ecuaciones diferenciales estocásticas. Cursos y Seminarios, Serie B, Departamento de Matemática, Fascículo 1, 2006 (in spanish). pdf (648KB)

PhD Dissertation

  1. A free boundary problem in combustion theory. Universidad de Buenos Aires, 2002. pdf (525KB)

 

Teaching

Courses (past semesters):

Human Resources Training

Undergraduate Students:

  • Leandro Del Pezzo: Tesis de Licenciatura, Un problema de optimización para el primer autovalor del p-Laplaciano más un potencial (2005). pdf (in spanish).
  • Analía Silva: Tesis de Licenciatura, Multiplicidad de soluciones para ecuaciones elípticas no lineales con exponente crítico (2008). pdf (in spanish).
  • Carla Baroncini: Tesis de Licenciatura, Estudio de medidas capacitarias asociadas a espacios de Sobolev con exponente variable (2013). pdf (in spanish).
  • Antonella Ritorto: Tesis de Licenciatura, Algunos problemas de optimización de forma (2014). pdf (in spanish).

Graduate Students:

  • Leandro Del Pezzo: PhD Thesis, Some optimization problems for the p-Laplace operator (2009). pdf
  • Ariel Salort: (co-directed with Juan Pablo Pinasco) PhD Thesis, Eigenvalue homogenization for quasilinear elliptic equations (2012). pdf
  • Analía Silva: PhD Thesis, Elliptic problems with nonstadard growth and lack of compactness (2013). pdf
  • Juan Spedaletti:
    • Master Thesis, Un problema de diseño óptimo asociado al primer autovalor de Steklov (2015). pdf (in spanish).
    • PhD Thesis, Asymptotic behavior of optimal design problems in local and nonlocal models (2016). pdf (in spanish)
  • Antonella Ritorto: PhD Thesis, Homogenization and optimal design in nonlocal diffusion (2017).  pdf
  • Carla Baroncini: PhD Thesis, Nonlinear PDEs under domain perturbations (2018).  pdf
  • Adriana Aragón: PhD Thesis, Numerical methods for nonstandard growth elliptic differential equations and applications to image processing. (2024).  pdf

Prizes

Misha-Cotlar award to young mathematician in Argentina by the National Academy of Exact and Natural Sciences. Awarded