publications

Books (1)

  1. Nonlinear Reaction-Diffusion Processes for Nanocomposites
    D铆az, J.I.,聽 G贸mez-Castro, D.,聽and Shaposhnikova, T. A
    De Gruyter 2021

Preprints (2)

  1. P3
    Interpreting systems of continuity equations in spaces of probability measures through PDE duality
    Carrillo, Jos茅 A.,聽and G贸mez-Castro, David
    2022
  2. P2
    Asymptotic simplification of Aggregation-Diffusion equations towards the heat kernel
    Carrillo, Jos茅 A.,聽 G贸mez-Castro, D.,聽Yao, Yao,聽and Zeng, Chongchun
    2021

Journal Articles (33)

  1. J33
    Singular boundary behaviour and large solutions for fractional elliptic equations
    Abatangelo, Nicola,聽 G贸mez-Castro, D.,聽and V谩zquez, J.L.
    Journal of the London Mathematical Society Accepted for publication , 2022
  2. J32
    Singular solutions for fractional parabolic boundary value problems
    Chan, Hardy,聽 G贸mez-Castro, David,聽and V谩zquez, Juan Luis
    Revista de la Real Academia de Ciencias Exactas, F谋虂sicas y Naturales. Serie A. Matem谩ticas 116 (4), 2022
  3. J31
    A fast regularisation of a Newtonian vortex equation
    Carrillo, Jos茅 A.,聽 G贸mez-Castro, D.,聽and V谩zquez, J.L.
    Annales de l鈥橧nstitut Henri Poincar茅 C, Analyse non lin茅aire , 2022
  4. J30
    Vortex formation for a non-local interaction model with Newtonian repulsion and superlinear mobility
    Carrillo, Jose A.,聽 G贸mez-Castro, David,聽and V谩zquez, Juan Luis
    Advances in Nonlinear Analysis 11 (1), 2022
  5. J29
    Infinite-time concentration in aggregation鈥揹iffusion equations with a given potential
    Carrillo, J.A.,聽 G贸mez-Castro, D.,聽and V谩zquez, J.L.
    Journal de Math茅matiques Pures et Appliqu茅es 157 , 2022
  6. J28
    Three representations of the fractional p-Laplacian: Semigroup, extension and Balakrishnan formulas
    del Teso, F茅lix,聽 G贸mez-Castro, D.,聽and V谩zquez, J.L.
    Fract. Calc. Appl. Anal. 24 (4), 2021
  7. J27
    Characterisation of homogeneous fractional Sobolev spaces
    Brasco, Lorenzo,聽 G贸mez-Castro, D.,聽and V谩zquez, J.L.
    Calculus of Variations and Partial Differential Equations 60 (2), 2021
  8. J26
    Steiner symmetrization for anisotropic quasilinear equations via partial discretization
    Brock, Friedemann,聽D铆az, J.I.,聽Ferone, Adele,聽 G贸mez-Castro, D.,聽and Mercaldo, Anna
    Annales de l鈥橧nstitut Henri Poincar茅 C, Analyse non lin茅aire 38 (2), 2021
  9. J25
    Blow-up phenomena in nonlocal eigenvalue problems: When theories of L^1 and L^2 meet
    Chan, Hardy,聽 G贸mez-Castro, D.,聽and V谩zquez, J.L.
    Journal of Functional Analysis 280 (7), 2021
  10. J24
    Estimates on translations and Taylor expansions in fractional Sobolev spaces
    del Teso, F茅lix,聽 G贸mez-Castro, D.,聽and V谩zquez, J.L.
    Nonlinear Anal. 200 , 2020
  11. 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
    D铆az, J. I.,聽 G贸mez-Castro, D.,聽Shaposhnikova, T. A.,聽and Zubova, M. N.
    Dokl. Math. 101 (2), 2020
  12. J22
    Homogenization of a net of periodic critically scaled boundary obstacles related to reverse osmosis 鈥渘ano-composite鈥 membranes
    D铆az, J.I.,聽 G贸mez-Castro, D.,聽Podolskiy, Alexander V,聽and Shaposhnikova, T. A
    Adv. Nonlinear Anal. 9 (1), 2020
  13. J21
    The fractional Schr枚dinger equation with singular potential and measure data
    G贸mez-Castro, D.,聽and V谩zquez, J.L.
    Discret. Contin. Dyn. Syst. - A 39 (12), 2019
  14. J20
    A nonlocal memory strange term arising in the critical scale homogenisation of a diffusion equation with a dynamic boundary condition
    D铆az, J.I.,聽 G贸mez-Castro, D.,聽Shaposhnikova, T. A.,聽and Zubova, Maria N.
    Electron. J. Differ. Equ. 2019 (77), 2019
  15. J18
    Characterizing the strange term in critical size homogenization: Quasilinear equations with a general microscopic boundary condition
    D铆az, J. I.,聽 G贸mez-Castro, D.,聽Podol鈥檚kii, Alexander V,聽and Shaposhnikova, T. A
    Adv. Nonlinear Anal. 8 (1), 2019
  16. J17
    Classification of homogenized limits of diffusion problems with spatially dependent reaction over critical-size particles
    D铆az, J. I.,聽 G贸mez-Castro, D.,聽Shaposhnikova, T. A.,聽and Zubova, M. N.
    Appl. Anal. 98 (1-2), 2019
  17. J19
    On the well-posedness of a multiscale mathematical model for Lithium-ion batteries
    D铆az, J. I.,聽 G贸mez-Castro, D.,聽and Ramos, Angel M.
    Adv. Nonlinear Anal. 8 (1), 2018
  18. J16
    The fractional Schr枚dinger equation with general nonnegative potentials. The weighted space approach
    D铆az, J. I.,聽 G贸mez-Castro, D.,聽and V谩zquez, J. L.
    Nonlinear Anal. 177 , 2018
  19. J15
    Homogenization of Boundary Value Problems in Plane Domains with Frequently Alternating Type of Nonlinear Boundary Conditions: Critical Case
    D铆az, J. I.,聽 G贸mez-Castro, D.,聽Podolskiy, A. V.,聽and Shaposhnikova, T. A.
    Dokl. Math. 97 (3), 2018
  20. J14
    Study of tumor growth indicates the existence of an 鈥渋mmunological threshold鈥 separating states of pro- and antitumoral peritumoral inflammation
    Br煤, Antonio,聽 G贸mez-Castro, D.,聽Vila, Luis,聽Br煤, Isabel,聽and Souto, Juan Carlos
    PLoS One 13 (11), 2018
  21. 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
    D铆az, J. I.,聽 G贸mez-Castro, D.,聽Podolskii, A. V.,聽and Shaposhnikova, T. A.
    Rev. la Real Acad. Ciencias Exactas, F铆sicas y Nat. Ser. A. Matem谩ticas 112 (2), 2018
  22. J12
    Existence and uniqueness of solutions of Schr枚dinger type stationary equations with very singular potentials without prescribing boundary conditions and some applications
    D铆az, J.I.,聽 G贸mez-Castro, D.,聽and Rakotoson, J.-M.
    Differ. Equations Appl. 10 (1), 2018
  23. J11
    Linear diffusion with singular absorption potential and/or unbounded convective flow: The weighted space approach
    Temam, R.,聽Rakotoson, J. M.,聽 G贸mez-Castro, D.,聽and D铆az, J. I.
    Discrete and Continuous Dynamical Systems 38 (2), 2018
  24. J10
    Change of homogenized absorption term in diffusion processes with reaction on the boundary of periodically distributed asymmetric particles of critical size
    D铆az, J.I.,聽 G贸mez-Castro, D.,聽Shaposhnikova, T. A.,聽and Zubova, M. N.
    Electronic Journal of Differential Equations 2017 (178), 2017
  25. J09
    On the asymptotic limit of the effectiveness of reaction鈥揹iffusion equations in periodically structured media
    D铆az, J.I.,聽 G贸mez-Castro, D.,聽Podolskii, A.V.,聽and Shaposhnikova, T.A.
    Journal of Mathematical Analysis and Applications 455 (2), 2017
  26. J08
    Homogenization of variational inequalities of Signorini type for the p-Laplacian in perforated domains when p 鈭(1, 2)
    D铆az, J.I.,聽 G贸mez-Castro, D.,聽Podol鈥檚kii, A. V.,聽and Shaposhnikova, T. A.
    Doklady Mathematics 95 (2), 2017
  27. J07
    Visibility to discern local from nonlocal dynamic processes
    Br煤, Antonio,聽 G贸mez-Castro, D.,聽and Nu帽o, J.C.
    Physica A: Statistical Mechanics and its Applications 471 , 2017
  28. J06
    Shape differentiation of a steady-state reaction-diffusion problem arising in Chemical Engineering: the case of non-smooth kinetic with dead core
    G贸mez-Castro, D.
    Electronic Journal of Differential Equations 2017 (221), 2017
  29. J05
    Rigidity of optimal bases for signal spaces
    Brezis, Ha茂m,聽and G贸mez-Castro, D.
    Comptes Rendus Mathematique 355 (7), 2017
  30. 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
    D铆az, J.I.,聽 G贸mez-Castro, D.,聽Podol鈥檚kii, A. V.,聽and Shaposhnikova, T. A.
    Doklady Mathematics 94 (1), 2016
  31. J03
    On the Effectiveness of Wastewater Cylindrical Reactors: an Analysis Through Steiner Symmetrization
    D铆az, J.I.,聽and G贸mez-Castro, D.
    Pure and Applied Geophysics 173 (3), 2016
  32. J02
    The Effectiveness Factor of Reaction-Diffusion Equations: Homogenization and Existence of Optimal Pellet Shapes
    D铆az, J.I.,聽 G贸mez-Castro, D.,聽and Timofte, Claudia
    Journal of Elliptic and Parabolic Equations 2 (1-2), 2016
  33. J01
    An Application of Shape Differentiation to the Effectiveness of a Steady State Reaction-Diffusion Problem Arising in Chemical Engineering
    D铆az, J.I.,聽and G贸mez-Castro, D.
    Electronic Journal of Differential Equations 22 , 2015

Conference Proceedings

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

Thesis

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