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:
- I. Ceresa Dussel, J. Fernández Bonder and A. Silva. A priori estimates for solutions of $g-$Laplace type problems pdf
- J. Fernández Bonder and A. Silva. The concentration-compactness principle for Orlicz spaces and applications. pdf
- J. Fernández Bonder and A.M. Salort. Asymptotic behavior for anisotropic fractional energies. pdf
- A. Aragón, J. Fernández Bonder and D. Rubio. Effective numerical computations of p(x)--Laplace equations in 2D. pdf
In Press:
- 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
- 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:
- 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
- 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
- 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
- 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
- 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
- J. Fernández Bonder and A.M. Salort. Magnetic fractional order Orlicz-Sobolev spaces. Studia Mathematica, 259 (2021), 1--24. pdf
- 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
- J. Fernández Bonder and A.M. Salort Stability of solutions for nonlocal problems. Nonlinear Analysis, 200 (2020), 112080. pdf
- 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
- J. Fernández Bonder and A.M. Salort. Fractional order Orlicz-Sobolev spaces. J. Functional Anal. 277 (2019), no. 2, 333--367. pdf
- 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
- 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
- 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
- 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
- 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
- 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
- J. Fernández Bonder and J.F. Spedaletti. Some nonlocal optimal design problems. J. Math. Anal. Appl., 459 (2018), no. 2, 906--931. pdf
- 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
- 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
- J. Fernández Bonder, J.P. Pinasco and A.M. Salort. Homogenization of Fucik eigencurves. Mediterr. J. Math., 14 (2017), no. 2, 14--90. pdf
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- J. Fernández Bonder, J.P. Pinasco and A.M. Salort. Quasilinear eigenvalues. Rev. Un. Mat. Argentina 56 (2015), no. 1, 1--25.pdf
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- J. Fernández Bonder and J.P. Pinasco. Precise asymtotic of eigenvalues of resonant quasilinear systems. J. Differential Equations, 249 (2010), 136--150. pdf
- 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
- L. Del Pezzo and J. Fernández Bonder. Remarks on an optimization problem for the $p-$Laplacian. Appl. Math. Lett., 23 (2010), 188--192. pdf
- 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
- 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
- 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
- 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
- L. Del Pezzo and J. Fernández Bonder. Some optimization problems for p-Laplacian type equations. Appl. Math. Optim., 59 (2009), 365--381. pdf
- J. Fernández Bonder and P. Groisman. Time--space white noise eliminates global solutions in reaction diffusion equations. Physica D, 238 (2009), 209--215. pdf
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- J. Fernández Bonder. Multiple positive solutions for quasilinear elliptic problems with sign-changing nonlinearities. Abstr. Appl. Anal. 2004 (2004), no. 12, 1047--1056. pdf
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- J. Fernández Bonder and J.D. Rossi. Blow-up vs. spurious steady solutions. Proc. Amer. Math. Soc., 129 (2001), no. 1, 139--144. pdf
- 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
- 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
- J. Fernández Bonder and N. Wolanski. A free boundary problem in combustion theory. Interfaces Free Bound., 2 (2000), 381--411. pdf
- 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
- 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
- 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
- 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)
- 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
- A free boundary problem in combustion theory. Universidad de Buenos Aires, 2002. pdf (525KB)
Teaching
- 1st sem. 2023, Nonlinear PDEs.
- 2nd sem. 2022, Introduction to Continuous Modeling.
- 1st sem. 2022, Analysis I.
- 2nd sem. 2021, Analysis I.
- 2nd sem. 2020, Analysis I.
- 1st sem. 2020, Analysis I.
- 2nd sem. 2019, Partial Differential Equations and Analysis II.
- 1st sem. 2019, Functional Analysis.
- 2nd sem. 2018,
- aug-sep: Non Local Equations and Fractional Calculus.
- oct-dec: Visiting professor at UNNC.
- 1st sem. 2018, Partial Differential Equations.
- 2nd sem. 2017, Mathematics 2 (Linear Algebra for Physics).
- 1st sem. 2017, Real Analysis - Measure and Probability.
- 2nd sem. 2016, Partial Differential Equations.
- 1st sem. 2016, Functional Analysis.
- 2nd sem. 2015, Gamma-convergence and Applications.
- 1st sem. 2015, Partial Differential Equations.
- 2nd sem. 2014, Analysis II.
- 1st sem. 2014, Analysis I.
- 2nd sem. 2013, Optimal Transportation.
- 1st sem. 2013, (at UNSL) Nonlinear PDEs.
- 2nd sem. 2012, Analysis I.
- 1st sem. 2012, Partial Differential Equations.
- 2nd sem. 2011, Shape Optimization Problems.
- 1st sem. 2011, Analysis II.
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:
- Antonella Ritorto: PhD Thesis, Homogenization and optimal design in nonlocal diffusion (2017). pdf
- Carla Baroncini: PhD Thesis, Nonlinear PDEs under domain perturbations (2018). pdf
Prizes
Misha-Cotlar award to young mathematician in Argentina by the National Academy of Exact and Natural Sciences. Awarded