30 citations · 98 across the 17 of their papers we have counts for
18 papers
Interpreting systems of continuity equations in spaces of probability measures through PDE duality
José A. Carrillo, David Gómez-Castro
We introduce a notion of duality solution for a single or a system of transport equations in spaces of probability measures reminiscent of the viscosity solution notion for nonline…
Asymptotic simplification of Aggregation-Diffusion equations towards the heat kernel
José A. Carrillo, David Gómez-Castro, Yao Yao +1
We give sharp conditions for the large time asymptotic simplification of aggregation-diffusion equations with linear diffusion. As soon as the interaction potential is bounded and…
Infinite-time concentration in Aggregation--Diffusion equations with a given potential
Jose A. Carrillo, David Gómez-Castro, Juan Luis Vázquez
Typically, aggregation-diffusion is modeled by parabolic equations that combine linear or nonlinear diffusion with a Fokker-Planck convection term. Under very general suitable assu…
Three representations of the fractional -Laplacian: semigroup, extension and Balakrishnan formulas
Félix del Teso, David Gómez-Castro, Juan Luis Vázquez
We introduce three representation formulas for the fractional -Laplace operator in the whole range of parameters and . Note that for this a nonlinea…
Singular solutions for fractional parabolic boundary value problems
Hardy Chan, David Gómez-Castro, Juan Luis Vázquez
The standard problem for the classical heat equation posed in a bounded domain of is the initial and boundary value problem. If the Laplace operator is replaced b…
Characterisation of homogeneous fractional Sobolev spaces
Lorenzo Brasco, David Gómez-Castro, Juan Luis Vázquez
Our aim is to characterize the homogeneous fractional Sobolev-Slobodecki\uı spaces and their embeddings, for and . They are…
Estimates on translations and Taylor expansions in fractional Sobolev spaces
Félix del Teso, David Gómez-Castro, Juan Luis Vázquez
In this paper we study how the (normalised) Gagliardo semi-norms control translations. In particular, we prove that $\| u(\cdot + y) - u \|_{L^p (\ma…
Blow-up phenomena in nonlocal eigenvalue problems: when theories of and meet
Hardy Chan, David Gómez-Castro, Juan Luis Vázquez
We develop a linear theory of very weak solutions for nonlocal eigenvalue problems involving integro-differential operators posed in bounded domains with ho…
Steiner symmetrization for anisotropic quasilinear equations via partial discretization
Friedemann Brock, Jesús Ildefonso Díaz, Adele Ferone +2
In this paper we obtain comparison results for the quasilinear equation with homogeneous Dirichlet boundary conditions by Steiner rearrangement in variabl…
A fast regularisation of a Newtonian vortex equation
José A. Carrillo, David Gómez-Castro, Juan Luis Vázquez
We consider equations of the form , where is the Newtonian potential (inverse of the Laplacian) posed in the whole sp…
Singular boundary behaviour and large solutions for fractional elliptic equations
Nicola Abatangelo, David Gómez-Castro, Juan Luis Vázquez
We show that the boundary behaviour of solutions to nonlocal fractional equations posed in bounded domains strongly differs from the one of solutions to elliptic problems modelled…
A nonlocal memory strange term arising in the critical scale homogenisation of a diffusion equation with a dynamic boundary condition
Jesús Ildefonso Díaz, David Gómez-Castro, Tatiana A. Shaposhnikova +1
Our main interest in this paper is the study of homogenised limit of a parabolic equation with a nonlinear dynamic boundary condition of the micro-scale model set on a domain with…
The fractional Schrödinger equation with singular potential and measure data
David Gómez-Castro, Juan Luis Vázquez
We consider the steady fractional Schrödinger equation posed on a bounded domain ; is an integro-differential operator, like the usual versions of the fracti…
The fractional Schrödinger equation with general nonnegative potentials. The weighted space approach
Jesús Ildefonso Díaz, David Gómez-Castro, Juan Luis Vázquez
We study the Dirichlet problem for the stationary Schrödinger fractional Laplacian equation posed in bounded domain with zero outside c…
Homogenization and Shape Differentiation of Quasilinear Elliptic Equations
David Gómez-Castro
This thesis is divided into five chapters. The aim is the study of the effectiveness of a chemical as defined by R. Aris for semilinear elliptic equations. The first chapter focuse…
Linear diffusion with singular absorption potential and/or unbounded convective flow: the weighted space approach
Jesús Ildefonso Díaz, David Gómez-Castro, Jean-Michel Rakotoson +1
In this paper we prove the existence and uniqueness of very weak solutions to linear diffusion equations involving a singular absorption potential and/or an unbounded convective fl…
Existence and uniqueness of solutions of Schrödinger type stationary equations with very singular potentials without prescribing boundary conditions and some applications
Jesús Ildefonso Díaz, David Gómez-Castro, Jean-Michel Rakotoson
Motivated mainly by the localization over an open bounded set of of solutions of the Schrödinger equations, we consider the Schrödinger equation over with a v…
Shape differentiation of a steady-state reaction-diffusion problem arising in Chemical Engineering: the case of non-smooth kinetic with dead core
David Gómez-Castro
In this paper we consider an extension of the results in shape differentiation of semilinear equations with smooth nonlinearity presented in J.I. Díaz and D. Gómez-Castro: An Appli…