Institutos Universitarios

David Gómez Castro

Postdoctoral Research Associate


Profesor ayudante doctor (Assistant Professor) on leave
Department of Applied Mathematics and Mathematical Analysis
School of Mathematical Sciences
Complutense University of Madrid
Research Group MOMAT
Nonlinear PDEs and applications




I am a Postdoctoral Research Associate at the Mathematical Institute of the University of Oxford. I am on leave of my position as Assistant Professor at the Department of Applied Mathematics and Mathematical Analysis at Universidad Complutense de Madrid. . I completed my Ph.D. in Mathematical Engineering, Statistics and Operational Research under Prof. J.I. Díaz at Universidad Complutense de Madrid in 2017, supported by an FPU Grant. I received my M.Sc. and Bachelor Degrees in Mathematics from Universidad Complutense de Madrid. During 2018 I was Assistant Professor at the ICAI School of Engineering of Universidad Pontificia de Comillas. In 2018 I was awarded the Vicent Caselles Prize by RSME and Fundación BBVA.


Research interests

Local and non-local semilinear parabolic and elliptic problems (in particular Brézis’ theory of very weak solutions), homogenisation problems, rearrangement theory (Schwarz and Steiner), shape optimisation and differentiation.


Latest Publications

  • J. A. Carrillo, D. Gómez-Castro, J. Luis Vázquez, A fast regularisation of a Newtonian vortex equation, Annales de l'Institut Henri Poincaré C, 2022, vol. 39, nº3, pp.705-747 DOI 10.4171/AIHPC/17
  • J. A. Carrillo, D. Gómez-Castro, J. L. Vázquez. Vortex formation for a non-local interaction model with Newtonian repulsion and superlinear mobility. Advances in Nonlinear Analysis. 2022, 11, 1, 937 – 967.
  • L. Brasco, D. Gómez-Castro, J. L. Vázquez. Characterisation of homogeneous fractional Sobolev spaces. Calculus of Variations and Partial Differential Equations. 2021, 60, 2, Article number 60.
  • J. I. Díaz, D. Gómez-Castro, T. A. Shaposhnikova & M. N. Zubova. 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. Doklady Mathematics. 2020, 101, 96–101.
  • F. del Teso, D. Gómez-Castro, J. L. Vázquez. Estimates on translations and Taylor expansions in fractional Sobolev spaces. Nonlinear Analysis. 2020, 200, 111995.
  • F. Brock, J. I. Díaz, A. Ferone, D. Gómez-Castro, A. Mercaldo. Steiner symmetrization for anisotropic quasilinear equations via partial discretization. Annales de l’Institut Henri Poincaré C, Analyse non linéaire. 2020.
  • H. Chan, D. Gómez-Castro, J. L. Vázquez. Blow-up phenomena in nonlocal eigenvalue problems: When theories of L1 and L2 meet. Journal of Functional Analysis. Available online 11 November 2020, 108845. In Press, Corrected ProofWhat are Corrected Proof.
  • J. I. DíazD. Gómez-Castro, A. V. Podolskiy, T. A. Shaposhnikova. Homogenization of a net of periodic critically scaled boundary obstacles related to reverse osmosis “nano-composite” membranes. Advances in Nonlinear Analysis. 9(2020), no. 1, 193--227 doi:
  • J. I. DíazD. Gómez-Castro, A. V. Podol’skii, T. A. Shaposhnikova. Characterizing the strange term in critical size homogenization: Quasilinear equations with a general microscopic boundary condition. Advances in Nonlinear Analysis. 2019, 8, 679-693.
  • J. I. Díaz, D. Gómez-Castro, A. M. Ramos, On the well-posedness of a multiscale mathematical model for Lithium-ion batteries. Advances in Nonlinear Analysys, ISSN: 2191-9496, 2019; 8: 1132--1157. DOI link:
  • J. I. DíazD. Gómez-Castro, T. A. Shaposhnikova, M. N. Zubova. Classification of homogenized limits of diffusion problems with spatially dependent reaction over critical-size particles. Applicable Analysis, 98(1–2) (2019), 232–255.
  • J. I. Díaz, D. Gómez-Castro, T. A. Shaposhnikova, M. N. Zubova. A nonlocal memory strange term arising in the critical scale homogenization of diffusion equations with dynamic boundary conditions. Electronic Journal of Di erential Equations. Vol. 2019 (2019), No. 77, pp. 1--13. ISSN: 1072-6691. URL: or


Contact details 
Personal Webpage


J. I. Díaz, D. Gómez-Castro, T. A. Shaposhnikova. Nonlinear Reaction-Diffusion Processes for Nanocomposites: Anomalous Improved Homogenization. De Gruyter Series in Nonlinear Analysis and Applications. 2021. Hardcover ISBN: 9783110647273, eBook ISBN: 9783110648997