sample of publications

• articles 

  • A nonlinear diffusion equation with reaction localized in the half-line.  Mathematics in Engineering.  4:1-24. 2022
  • Extremals in Hardy-Littlewood-Sobolev inequalities for stable processes.  JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS.  507:1-18. 2022
  • Blow-up rates for a fractional heat equation.  PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY.  149:2011-2018. 2021
  • Anisotropic nonlocal diffusion equations with singular forcing.  ArXiv.org.  1-23. 2018
  • Regularity theory for singular nonlocal diffusion equations.  CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS.  57:136. 2018
  • Remarks on a nonlinear nonlocal operator in Orlicz spaces.  Advances in Nonlinear Analysis.  1-26. 2018
  • Grow-up for a quasilinear heat equation with a localized reaction in higher dimensions.  Revista Matematica Complutense.  31:805-832. 2018
  • Nonlocal heat equations: Regularizing effect, decay estimates and Nash inequalities.  COMMUNICATIONS ON PURE AND APPLIED ANALYSIS.  17:1161-1178. 2018
  • Nonlocal operators of order near zero.  JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS.  461:837-867. 2018
  • Grow-up for a quasilinear heat equation with a localized reaction.  Journal of Differential Equations.  1-19. 2018
  • Classical solutions and higher regularity for nonlinear fractional diffusion equations.  JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY.  19:1949-1975. 2017
  • Nonlocal filtration equations with rough kernels.  NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS.  137:402-425. 2016
  • Perturbations of a critical fractional equation.  PACIFIC JOURNAL OF MATHEMATICS.  271:65-85. 2014
  • Classical solutions for a logarithmic fractional diffusion equation.  JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES.  101:901-924. 2014
  • Nonlocal heat equations: decay estimates and Nash inequalities.  ArXiv.org.  2013
  • A concave-convex elliptic problem involving the fractional Laplacian.  PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS.  1:39-71. 2013
  • The Cauchy problem for a nonhomogeneous heat equation with reaction.  DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS.  33:643-662. 2013
  • Critical exponents for a semilinear parabolic equation with variable reaction.  PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS.  142:1027-1042. 2012
  • A General Fractional Porous Medium Equation.  COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS.  65:1242-1284. 2012
  • On some critical problems for the fractional Laplacian operator.  Journal of Differential Equations.  252:6133-6162. 2012
  • A fractional porous medium equation.  ADVANCES IN MATHEMATICS.  226:1378-1409. 2011
  • Stability of the Blow-up Time and the Blow-up Set under Perturbations.  DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS.  26:43-46. 2010
  • Incomplete Quenching in a System of Heat Equations Coupled at the Boundary.  JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS.  346:145-154. 2008

• conference contributions 

  • Nonlocal operators of order near zero 2017
  • Regularity theory for nonlocal filtration equations 2017
  • Classical solutions for nonlinear fractional diffusion equations 2014
  • Nonlocal heat equations: decay estimates and Nash inequalities 2014
  • Quenching for Systems: Numerical Approximations and Possible Analytical Continuation 2008