Juan-Davila

Juan Davila

PhD in Mathematics, Rutgers University, United States (2002)
Civil Engineering in Mathematics, Universidad de Chile (1996)

Position: Full Professor

Institution: Departamento de Ingeniería Matemática & Centro de Modelamiento Matemático (CMM),

Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile.

Research area: Nonlinear Analysis.

Contact:

Email: jdavila@dim.uchile.cl

Phone: +56 2 2978 4900

Adress: Beauchef 851, North Building, 5th floor, Santiago, Chile.

Publications

  • Dávila, Juan; Guerra, Ignacio; Slowly decaying radial solutions of an elliptic equation with subcritical and supercritical exponents. J. Anal. Math. 129 (2016), 367–391. pdf
  • Cinti, Eleonora; Davila, Juan; Del Pino, Manuel; Solutions of the fractional Allen–Cahn equation which are invariant under screw motion. J. Lond. Math. Soc. (2) 94 (2016), no. 1, 295–313. pdf
  • Chen, Wenjing; Dávila, Juan; Guerra, Ignacio Bubble tower solutions for a supercritical elliptic problem in RN. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 15 (2016), 85–116. pdf
  • Dávila, Juan; del Pino, Manuel; Dipierro, Serena; Valdinoci, Enrico Nonlocal Delaunay surfaces. Nonlinear Anal. 137 (2016), 357–380. pdf
  • Dávila, Juan; Wang, Kelei; Wei, Juncheng Qualitative analysis of rupture solutions for a MEMS problem. Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016), no. 1, 221–242. pdf
  • Dávila, Juan; del Pino, Manuel; Dipierro, Serena; Valdinoci, Enrico Concentration phenomena for the nonlocal Schrödinger equation with Dirichlet datum. Anal. PDE 8 (2015), no. 5, 1165–1235. pdf
  • Dávila, Juan; Pistoia, Angela; Vaira, Giusi. Bubbling solutions for supercritical problems on manifolds. J. Math. Pures Appl. (9) 103 (2015), no. 6, 1410–1440. pdf
  • Abdellaoui, B.; Biroud, K.; Davila, J.; Mahmoudi, F. Nonlinear elliptic problem related to the Hardy inequality with singular term at the boundary. Commun. Contemp. Math. 17 (2015), no. 3, 1450033, 28 pp. pdf
  • Dávila, Juan; Dupaigne, Louis; Wang, Kelei; Wei, Juncheng. A monotonicity formula and a Liouville-type theorem for a fourth order supercritical problem. Adv. Math. 258 (2014), 240–285. pdf
  • Dávila, Juan; Goubet, Olivier. Partial regularity for a Liouville system. Discrete Contin. Dyn. Syst. 34 (2014), no. 6, 2495–2503. pdf
  • Dávila, Juan; del Pino, Manuel; Wei, Juncheng. Concentrating standing waves for the fractional nonlinear Schrödinger equation. J. Differential Equations 256 (2014), no. 2, 858–892. pdf
  • Dávila, Juan; del Pino, Manuel; Sire, Yannick Nondegeneracy of the bubble in the critical case for nonlocal equations. Proc. Amer. Math. Soc. 141 (2013), no. 11, 3865–3870. pdf
  • Dávila, Juan; Flores, Isabel; Guerra, Ignacio. Multiplicity and singular solutions for a Liouville-type system in a ball. Adv. Differential Equations 18 (2013), no. 9-10, 797–824.
  • Chen, Wenjing; Dávila, Juan. Resonance phenomenon for a Gelfand-type problem.Nonlinear Anal. 89 (2013), 299–321. 35J91 (35B07). pdf
  • Dávila, Juan; López, Luis F. Regular solutions to a supercritical elliptic problem in exterior domains. J. Differential Equations 255 (2013), no. 4, 701–727. pdf
  • Coville, Jérôme; Dávila, Juan; Martínez, Salomé. Pulsating fronts for nonlocal dispersion and KPP nonlinearity. Ann. Inst. H. Poincaré Anal. Non Linéaire 30 (2013), no. 2, 179–223. pdf
  • Dávila, Juan; del Pino, Manuel; Guerra, Ignacio. Non-uniqueness of positive ground states of non-linear Schrödinger equations. Proc. Lond. Math. Soc. (3) 106 (2013), no. 2, 318–344. pdf
  • Dávila, Juan; Ye, Dong. On finite Morse index solutions of two equations with negative exponent. Proc. Roy. Soc. Edinburgh Sect. A 143 (2013), no. 1, 121–128. (Reviewer: Vesa Julin) 35J75 (35B09 35J91 58E05). pdf
  • Castro, Hernán; Dávila, Juan; Wang, Hui. A Hardy type inequality for Wm,10(Ω)functions. J. Eur. Math. Soc. (JEMS) 15 (2013), no. 1, 145–155.
  • Dávila, Juan; Wei, Juncheng Point ruptures for a MEMS equation with fringing field.Comm. Partial Differential Equations 37 (2012), no. 8, 1462–1493. pdf
  • Dávila, Juan; Montenegro, Marcelo. Concentration for an elliptic equation with singular nonlinearity. J. Math. Pures Appl. (9) 97 (2012), no. 6, 545–578. pdf
  • Cosner, Chris; Dávila, Juan; Martínez, Salome Evolutionary stability of ideal free nonlocal dispersal. J. Biol. Dyn. 6 (2012), no. 2, 395–405. pdf
  • Dávila, Juan; Topp, Erwin. Concentrating solutions of the Liouville equation with Robin boundary condition. J. Differential Equations 252 (2012), no. 3, 2648–2697. pdf
  • Castro, Hernán; Dávila, Juan; Wang, Hui A Hardy type inequality for W2,10(Ω)functions. C. R. Math. Acad. Sci. Paris 349 (2011), no. 13-14, 765–767.
  • Capella, Antonio; Dávila, Juan; Dupaigne, Louis; Sire, Yannick. Regularity of radial extremal solutions for some non-local semilinear equations. Comm. Partial Differential Equations 36 (2011), no. 8, 1353–1384. pdf
  • Coville, Jérôme; Dávila, Juan Existence of radial stationary solutions for a system in combustion theory. Discrete Contin. Dyn. Syst. Ser. B 16 (2011), no. 3, 739–766. pdf
  • Dávila, Juan; Peral, Ireneo. Nonlinear elliptic problems with a singular weight on the boundary. Calc. Var. Partial Differential Equations 41 (2011), no. 3-4, 567–586. pdf
  • Dávila, Juan; Dupaigne, Louis; Farina, Alberto Partial regularity of finite Morse index solutions to the Lane-Emden equation. J. Funct. Anal. 261 (2011), no. 1, 218–232. pdf
  • Dávila, Juan; del Pino, Manuel; Musso, Monica Bistable boundary reactions in two dimensions. Arch. Ration. Mech. Anal. 200 (2011), no. 1, 89–140. pdf
  • Dávila, Juan; Montenegro, Marcelo. Remarks on positive and free boundary solutions to a singular equation. Rev. Integr. Temas Mat. 28 (2010), no. 2, 85–100. pdf
  • Dávila, Juan; Flores, Isabel; Guerra, Ignacio Multiplicity of solutions for a fourth order equation with power-type nonlinearity. Math. Ann. 348 (2010), no. 1, 143–193. pdf
  • Dávila, Juan; Flores, Isabel; Guerra, Ignacio. Multiplicity of solutions for a fourth order problem with exponential nonlinearity. J. Differential Equations 247 (2009), no. 11, 3136–3162. pdf
  • Dávila, Juan; Dupaigne, Louis; Goubet, Olivier; Martínez, Salomé. Boundary blow-up solutions of cooperative systems. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 5, 1767–1791. pdf
  • Dávila, Juan; Montenegro, Marcelo. Radial solutions of an elliptic equation with singular nonlinearity. J. Math. Anal. Appl. 352 (2009), no. 1, 360–379. pdf
  • Dávila, J. Singular solutions of semi-linear elliptic problems. Handbook of differential equations: stationary partial differential equations. Vol. VI, 83–176, Handb. Differ. Equ., Elsevier/North-Holland, Amsterdam, 2008. pdf
  • Dávila, Juan; Kowalczyk, Michał; Montenegro, Marcelo. Critical points of the regular part of the harmonic Green function with Robin boundary condition. J. Funct. Anal.255 (2008), no. 5, 1057–1101. pdf
  • Coville, Jérôme; Dávila, Juan; Martínez, Salomé Nonlocal anisotropic dispersal with monostable nonlinearity. J. Differential Equations 244 (2008), no. 12, 3080–3118. pdf
  • Dávila, Juan; del Pino, Manuel; Musso, Monica; Wei, Juncheng Fast and slow decay solutions for supercritical elliptic problems in exterior domains. Calc. Var. Partial Differential Equations 32 (2008), no. 4, 453–480.  pdf
  • Dávila, Juan; Dupaigne, Louis; Montenegro, Marcelo The extremal solution of a boundary reaction problem. Commun. Pure Appl. Anal. 7 (2008), no. 4, 795–817.pdf
  • Dávila, Juan; Ponce, Augusto C. Hausdorff dimension of ruptures sets and removable singularities. C. R. Math. Acad. Sci. Paris 346 (2008), no. 1-2, 27–32. pdf
  • Coville, Jérôme; Dávila, Juan; Martínez, Salomé Existence and uniqueness of solutions to a nonlocal equation with monostable nonlinearity. SIAM J. Math. Anal. 39 (2008), no. 5, 1693–1709. pdf
  • Dávila, J.; Dupaigne, L. Perturbing singular solutions of the Gelfand problem.Commun. Contemp. Math. 9 (2007), no. 5, 639–680. pdf
  • Dávila, Juan; del Pino, Manuel; Musso, Monica. The supercritical Lane-Emden-Fowler equation in exterior domains. Comm. Partial Differential Equations 32 (2007), no. 7-9, 1225–1243. pdf
  • Dávila, Juan; Dupaigne, Louis; Guerra, Ignacio; Montenegro, Marcelo Stable solutions for the bilaplacian with exponential nonlinearity. SIAM J. Math. Anal. 39 (2007), no. 2, 565–592. pdf
  • Dávila, Juan; del Pino, Manuel; Musso, Monica; Wei, Juncheng. Standing waves for supercritical nonlinear Schrödinger equations. J. Differential Equations 236 (2007), no. 1, 164–198. pdf
  • Dávila, Juan; del Pino, Manuel; Musso, Monica; Wei, Juncheng. Singular limits of a two-dimensional boundary value problem arising in corrosion modelling. Arch. Ration. Mech. Anal. 182 (2006), no. 2, 181–221. pdf
  • Dávila, Juan; Montenegro, Marcelo. Hölder estimates for solutions to a singular nonlinear Neumann problem. Elliptic and parabolic problems, 189–205, Progr. Nonlinear Differential Equations Appl., 63, Birkhäuser, Basel, 2005. pdf
  • Dávila, Juan; del Pino, Manuel; Musso, Monica Concentrating solutions in a two-dimensional elliptic problem with exponential Neumann data. J. Funct. Anal. 227 (2005), no. 2, 430–490. pdf
  • Dávila, Juan; Bonder, Julian Fernández; Rossi, Julio D.; Groisman, Pablo; Sued, Mariela. Numerical analysis of stochastic differential equations with explosions.Stoch. Anal. Appl. 23 (2005), no. 4, 809–825. pdf
  • Dávila, Juan; Montenegro, Marcelo Nonlinear problems with solutions exhibiting a free boundary on the boundary. Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2005), no. 3, 303–330.
  • Dávila, Juan; Montenegro, Marcelo. Existence and asymptotic behavior for a singular parabolic equation. Trans. Amer. Math. Soc. 357 (2005), no. 5, 1801–1828.
  • Dávila, Juan; Rossi, Julio D. Self-similar solutions of the porous medium equation in a half-space with a nonlinear boundary condition: existence and symmetry. J. Math. Anal. Appl. 296 (2004), no. 2, 634–649. pdf
  • Dávila, J.; Dupaigne, L. Hardy-type inequalities. J. Eur. Math. Soc. (JEMS) 6 (2004), no. 3, 335–365.
  • Dávila, Juan. Global regularity for a singular equation and local H1 minimizers of a nondifferentiable functional. Commun. Contemp. Math. 6 (2004), no. 1, 165–193. pdf
  • Dávila, Juan; Ponce, Augusto C. Variants of Kato’s inequality and removable singularities. J. Anal. Math. 91 (2003), 143–178. pdf
  • Dávila, Juan; Montenegro, Marcelo A singular equation with positive and free boundary solutions. RACSAM. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 97 (2003), no. 1, 107–112. pdf
  • Dávila, Juan; Montenegro, Marcelo Positive versus free boundary solutions to a singular elliptic equation. J. Anal. Math. 90 (2003), 303–335. pdf
  • Dávila, Juan; Ignat, Radu Lifting of BV functions with values in S1. C. R. Math. Acad. Sci. Paris 337 (2003), no. 3, 159–164. pdf
  • Dávila, Juan; Dupaigne, Louis Comparison results for PDEs with a singular potential.Proc. Roy. Soc. Edinburgh Sect. A 133 (2003), no. 1, 61–83. pdf
  • Dávila, J. On an open question about functions of bounded variation. Calc. Var. Partial Differential Equations 15 (2002), no. 4, 519–527. pdf
  • Dávila, Juan. A nonlinear elliptic equation with rapidly oscillating boundary conditions. Asymptot. Anal. 28 (2001), no. 3-4, 279–307. pdf
  • Dávila, Juan. A strong maximum principle for the Laplace equation with mixed boundary condition. J. Funct. Anal. 183 (2001), no. 1, 231–244. pdf
  • Dávila, Juan Some extremal singular solutions of a nonlinear elliptic equation.Differential Integral Equations 14 (2001), no. 3, 289–304. pdf
  • Conca, Carlos; Davila, Juan. Optimal bounds for mixtures of infinitely many materials. Numerical methods in mechanics (Concepción, 1995), 59–69, Pitman Res. Notes Math. Ser., 371, Longman, Harlow, 1997.