publications

Books (1)

  1. Nonlinear Reaction-Diffusion Processes for Nanocomposites
    Díaz, J.I.Gómez-Castro, D., and Shaposhnikova, T. A
    De Gruyter 2021

Preprints (2)

  1. P1
    Interpreting systems of continuity equations in spaces of probability measures through PDE duality
    Carrillo, José A., and Gómez-Castro, David
    2022
  2. P2
    Failure of the strong maximum principle for linear elliptic with singular convection of non-negative divergence
    Boccardo, Lucio,  Gómez-Castro, David, and Díaz, Jesús Ildefonso
    2022

Journal Articles (34)

  1. J34
    Asymptotic simplification of Aggregation-Diffusion equations towards the heat kernel
    Carrillo, José A.Gómez-Castro, D.Yao, Yao, and Zeng, Chongchun
    Archive for Rational Mechanics and Analysis Accepted for publication , 2023
  2. J33
    Singular boundary behaviour and large solutions for fractional elliptic equations
    Abatangelo, NicolaGómez-Castro, D., and Vázquez, J.L.
    Journal of the London Mathematical Society Accepted for publication , 2022
  3. J32
    Singular solutions for fractional parabolic boundary value problems
    Chan, HardyGómez-Castro, David, and Vázquez, Juan Luis
    Revista de la Real Academia de Ciencias Exactas, Fı́sicas y Naturales. Serie A. Matemáticas 116 (4), 2022
  4. J31
    A fast regularisation of a Newtonian vortex equation
    Carrillo, José A.Gómez-Castro, D., and Vázquez, J.L.
    Annales de l’Institut Henri Poincaré C, Analyse non linéaire , 2022
  5. J30
    Vortex formation for a non-local interaction model with Newtonian repulsion and superlinear mobility
    Carrillo, Jose A.Gómez-Castro, David, and Vázquez, Juan Luis
    Advances in Nonlinear Analysis 11 (1), 2022
  6. J29
    Infinite-time concentration in aggregation–diffusion equations with a given potential
    Carrillo, J.A.Gómez-Castro, D., and Vázquez, J.L.
    Journal de Mathématiques Pures et Appliquées 157 , 2022
  7. J28
    Three representations of the fractional p-Laplacian: Semigroup, extension and Balakrishnan formulas
    del Teso, FélixGómez-Castro, D., and Vázquez, J.L.
    Fract. Calc. Appl. Anal. 24 (4), 2021
  8. J27
    Characterisation of homogeneous fractional Sobolev spaces
    Brasco, Lorenzo,  Gómez-Castro, D., and Vázquez, J.L.
    Calculus of Variations and Partial Differential Equations 60 (2), 2021
  9. J26
    Steiner symmetrization for anisotropic quasilinear equations via partial discretization
    Brock, FriedemannDíaz, J.I., Ferone, Adele,  Gómez-Castro, D., and Mercaldo, Anna
    Annales de l’Institut Henri Poincaré C, Analyse non linéaire 38 (2), 2021
  10. J25
    Blow-up phenomena in nonlocal eigenvalue problems: When theories of L^1 and L^2 meet
    Chan, HardyGómez-Castro, D., and Vázquez, J.L.
    Journal of Functional Analysis 280 (7), 2021
  11. J24
    Estimates on translations and Taylor expansions in fractional Sobolev spaces
    del Teso, FélixGómez-Castro, D., and Vázquez, J.L.
    Nonlinear Anal. 200 , 2020
  12. J23
    A Time-Dependent Strange Term Arising in Homogenization of an Elliptic Problem with Rapidly Alternating Neumann and Dynamic Boundary Conditions Specified at the Domain Boundary: The Critical Case
    Díaz, J. I.Gómez-Castro, D., Shaposhnikova, T. A., and Zubova, M. N.
    Dokl. Math. 101 (2), 2020
  13. J22
    Homogenization of a net of periodic critically scaled boundary obstacles related to reverse osmosis “nano-composite” membranes
    Díaz, J.I.Gómez-Castro, D., Podolskiy, Alexander V, and Shaposhnikova, T. A
    Adv. Nonlinear Anal. 9 (1), 2020
  14. J21
    The fractional Schrödinger equation with singular potential and measure data
    Gómez-Castro, D., and Vázquez, J.L.
    Discret. Contin. Dyn. Syst. - A 39 (12), 2019
  15. J20
    A nonlocal memory strange term arising in the critical scale homogenisation of a diffusion equation with a dynamic boundary condition
    Díaz, J.I.Gómez-Castro, D., Shaposhnikova, T. A., and Zubova, Maria N.
    Electron. J. Differ. Equ. 2019 (77), 2019
  16. J18
    Characterizing the strange term in critical size homogenization: Quasilinear equations with a general microscopic boundary condition
    Díaz, J. I.Gómez-Castro, D., Podol’skii, Alexander V, and Shaposhnikova, T. A
    Adv. Nonlinear Anal. 8 (1), 2019
  17. J17
    Classification of homogenized limits of diffusion problems with spatially dependent reaction over critical-size particles
    Díaz, J. I.Gómez-Castro, D., Shaposhnikova, T. A., and Zubova, M. N.
    Appl. Anal. 98 (1-2), 2019
  18. J19
    On the well-posedness of a multiscale mathematical model for Lithium-ion batteries
    Díaz, J. I.Gómez-Castro, D., and Ramos, Angel M.
    Adv. Nonlinear Anal. 8 (1), 2018
  19. J16
    The fractional Schrödinger equation with general nonnegative potentials. The weighted space approach
    Díaz, J. I.Gómez-Castro, D., and Vázquez, J. L.
    Nonlinear Anal. 177 , 2018
  20. J15
    Homogenization of Boundary Value Problems in Plane Domains with Frequently Alternating Type of Nonlinear Boundary Conditions: Critical Case
    Díaz, J. I.Gómez-Castro, D., Podolskiy, A. V., and Shaposhnikova, T. A.
    Dokl. Math. 97 (3), 2018
  21. J14
    Study of tumor growth indicates the existence of an “immunological threshold” separating states of pro- and antitumoral peritumoral inflammation
    Brú, Antonio,  Gómez-Castro, D., Vila, Luis, Brú, Isabel, and Souto, Juan Carlos
    PLoS One 13 (11), 2018
  22. J13
    Non existence of critical scales in the homogenization of the problem with p-Laplace diffusion and nonlinear reaction in the boundary of periodically distributed particles in n-dimensional domains when p>n
    Díaz, J. I.Gómez-Castro, D., Podolskii, A. V., and Shaposhnikova, T. A.
    Rev. la Real Acad. Ciencias Exactas, Físicas y Nat. Ser. A. Matemáticas 112 (2), 2018
  23. J12
    Existence and uniqueness of solutions of Schrödinger type stationary equations with very singular potentials without prescribing boundary conditions and some applications
    Díaz, J.I.Gómez-Castro, D., and Rakotoson, J.-M.
    Differ. Equations Appl. 10 (1), 2018
  24. J11
    Linear diffusion with singular absorption potential and/or unbounded convective flow: The weighted space approach
    Temam, R., Rakotoson, J. M.,  Gómez-Castro, D., and Díaz, J. I.
    Discrete and Continuous Dynamical Systems 38 (2), 2018
  25. J10
    Change of homogenized absorption term in diffusion processes with reaction on the boundary of periodically distributed asymmetric particles of critical size
    Díaz, J.I.Gómez-Castro, D., Shaposhnikova, T. A., and Zubova, M. N.
    Electronic Journal of Differential Equations 2017 (178), 2017
  26. J09
    On the asymptotic limit of the effectiveness of reaction–diffusion equations in periodically structured media
    Díaz, J.I.Gómez-Castro, D., Podolskii, A.V., and Shaposhnikova, T.A.
    Journal of Mathematical Analysis and Applications 455 (2), 2017
  27. J08
    Homogenization of variational inequalities of Signorini type for the p-Laplacian in perforated domains when p ∈(1, 2)
    Díaz, J.I.Gómez-Castro, D., Podol’skii, A. V., and Shaposhnikova, T. A.
    Doklady Mathematics 95 (2), 2017
  28. J07
    Visibility to discern local from nonlocal dynamic processes
    Brú, Antonio,  Gómez-Castro, D., and Nuño, J.C.
    Physica A: Statistical Mechanics and its Applications 471 , 2017
  29. J06
    Shape differentiation of a steady-state reaction-diffusion problem arising in Chemical Engineering: the case of non-smooth kinetic with dead core
    Gómez-Castro, D.
    Electronic Journal of Differential Equations 2017 (221), 2017
  30. J05
    Rigidity of optimal bases for signal spaces
    Brezis, Haïm, and Gómez-Castro, D.
    Comptes Rendus Mathematique 355 (7), 2017
  31. J04
    Homogenization of the p-Laplace operator with nonlinear boundary condition on critical size particles: identifying the strange terms for some non smooth and multivalued operators
    Díaz, J.I.Gómez-Castro, D., Podol’skii, A. V., and Shaposhnikova, T. A.
    Doklady Mathematics 94 (1), 2016
  32. J03
    On the Effectiveness of Wastewater Cylindrical Reactors: an Analysis Through Steiner Symmetrization
    Díaz, J.I., and Gómez-Castro, D.
    Pure and Applied Geophysics 173 (3), 2016
  33. J02
    The Effectiveness Factor of Reaction-Diffusion Equations: Homogenization and Existence of Optimal Pellet Shapes
    Díaz, J.I.Gómez-Castro, D., and Timofte, Claudia
    Journal of Elliptic and Parabolic Equations 2 (1-2), 2016
  34. J01
    An Application of Shape Differentiation to the Effectiveness of a Steady State Reaction-Diffusion Problem Arising in Chemical Engineering
    Díaz, J.I., and Gómez-Castro, D.
    Electronic Journal of Differential Equations 22 , 2015

Conference Proceedings

  1. C01
    A mathematical proof in nanocatalysis: better homogenized results in the diffusion of a chemical reactant through critically small reactive particles
    Díaz, J.I., and Gómez-Castro, D.
    In Progress in Industrial Mathematics at ECMI 2016 2017
  2. C03
    On the influence of pellet shape on the effectiveness factor of homogenized chemical reactions
    Díaz, J.I.Gómez-Castro, D., and Timofte, Claudia
    In Proceedings Of The XXIV Congress On Differential Equations And Applications XIV Congress On Applied Mathematics 2015
  3. C02
    Steiner symmetrization for concave semilinear elliptic and parabolic equations and the obstacle problem
    Gómez-Castro, D., and Díaz, J.I.
    In Dynamical Systems and Differential Equations, Proceedings of the 10th AIMS International Conference (Madrid, Spain) 2015

Thesis

  1. 1. Gómez-Castro D (2017) Homogenization and Shape Differentiation of Quasilinear Elliptic Equations.