17 citations · 20 across the 7 of their papers we have counts for
10 papers
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…
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…
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…