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.

Papers in Scientific Journals

Submitted for Publications:

1. I. Ceresa Dussel, J. Fernández Bonder and A. Silva. A priori estimates for solutions of $g-$Laplace type problems pdf
2. J. Fernández Bonder and A. Silva. The concentration-compactness principle for Orlicz spaces and applications. pdf
3. J. Fernández Bonder and A.M. Salort. Asymptotic behavior for anisotropic fractional energies. pdf
4. A. Aragón, J. Fernández Bonder and D. Rubio. Effective numerical computations of p(x)--Laplace equations in 2D. pdf

In Press:

1. J. Fernández Bonder, A.M. Salort and H. Vivas. Global Hölder regularity for eigenfunctions of the fractional g-Laplacian. To appear in J. Math. Appl. Anal. pdf
2. 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. 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
2. 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
3. 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
4. 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
5. 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
6. J. Fernández Bonder and A.M. Salort. Magnetic fractional order Orlicz-Sobolev spaces. Studia Mathematica, 259 (2021), 1--24.   pdf
7. 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
8. J. Fernández Bonder and A.M. Salort Stability of solutions for nonlocal problems. Nonlinear Analysis, 200 (2020), 112080.   pdf
9. 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
10. J. Fernández Bonder and A.M. Salort. Fractional order Orlicz-Sobolev spaces. J. Functional Anal. 277 (2019), no. 2, 333--367. pdf
11. 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
12. 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
13. 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
14. 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
15. 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
16. 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
17. J. Fernández Bonder and J.F. Spedaletti.  Some nonlocal optimal design problems. J. Math. Anal. Appl., 459 (2018), no. 2, 906--931.   pdf
18. 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
19. 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
20. J. Fernández Bonder, J.P. Pinasco and A.M. Salort. Homogenization of Fucik eigencurves. Mediterr. J. Math., 14 (2017), no. 2, 14--90. pdf
21. 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
22. 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
23. 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
24. 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
25. 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
26. 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
27. 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
28. 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
29. J. Fernández Bonder, J.P. Pinasco and A.M. Salort. Quasilinear eigenvalues. Rev. Un. Mat. Argentina  56 (2015), no. 1, 1--25.pdf
30. 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
31. 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
32. 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
33. 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
34. 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
35. 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
36. 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
37. 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
38. J. Fernández Bonder and J.P. Pinasco. Precise asymtotic of eigenvalues of resonant quasilinear systems. J. Differential Equations, 249 (2010), 136--150. pdf
39. 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
40. L. Del Pezzo and J. Fernández Bonder. Remarks on an optimization problem for the $p-$Laplacian. Appl. Math. Lett., 23 (2010), 188--192. pdf
41. 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
42. 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
43. 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
44. 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
45. L. Del Pezzo and J. Fernández Bonder. Some optimization problems for p-Laplacian type equations. Appl. Math. Optim., 59 (2009), 365--381. pdf
46. J. Fernández Bonder and P. Groisman. Time--space white noise eliminates global solutions in reaction diffusion equations. Physica D, 238 (2009), 209--215. pdf
47. 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
48. 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
49. 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
50. 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
51. 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
52. 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
53. 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
54. 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
55. 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
56. 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
57. 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
58. 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
59. 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
60. 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
61. 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
62. 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
63. 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
64. J. Fernández Bonder. Multiple positive solutions for quasilinear elliptic problems with sign-changing nonlinearities. Abstr. Appl. Anal. 2004 (2004), no. 12, 1047--1056. pdf
65. 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
66. 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
67. 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
68. 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
69. 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
70. 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
71. 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
72. 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
73. 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
74. 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
75. 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
76. 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
77. 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
78. 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
79. J. Fernández Bonder and J.D. Rossi. Blow-up vs. spurious steady solutions. Proc. Amer. Math. Soc., 129 (2001), no. 1, 139--144. pdf
80. 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
81. 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
82. J. Fernández Bonder and N. Wolanski. A free boundary problem in combustion theory. Interfaces Free Bound., 2 (2000), 381--411. pdf
83. 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)

• 1^st sem. 2023, Nonlinear PDEs.
• 2^nd sem. 2022, Introduction to Continuous Modeling.
• 1^st sem. 2022, Analysis I.
• 2^nd sem. 2021, Analysis I.
• 2^nd sem. 2020, Analysis I.
• 1^st sem. 2020, Analysis I.
• 2^nd sem. 2019, Partial Differential Equations and Analysis II.
• 1^st sem. 2019, Functional Analysis.
• 2^nd sem. 2018,
  • aug-sep: Non Local Equations and Fractional Calculus.
  • oct-dec: Visiting professor at UNNC.
• 1^st sem. 2018, Partial Differential Equations.
• 2^nd sem. 2017, Mathematics 2 (Linear Algebra for Physics).
• 1^st sem. 2017, Real Analysis - Measure and Probability.
• 2^nd sem. 2016, Partial Differential Equations.
• 1^st sem. 2016, Functional Analysis.
• 2^nd sem. 2015, Gamma-convergence and Applications.
• 1^st sem. 2015, Partial Differential Equations.
• 2^nd sem. 2014, Analysis II.
• 1^st sem. 2014, Analysis I.
• 2^nd sem. 2013, Optimal Transportation.
• 1^st sem. 2013, (at UNSL) Nonlinear PDEs.
• 2^nd sem. 2012, Analysis I.
• 1^st sem. 2012, Partial Differential Equations.
• 2^nd sem. 2011, Shape Optimization Problems.
• 1^st sem. 2011, Analysis II.

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

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