70 citations · 313 across the 31 of their papers we have counts for
5 papers · 1 filter
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…
Asymptotic behaviour for the Heat Equation in Hyperbolic Space
Juan Luis Vázquez
Following the classical result of long-time asymptotic convergence towards the Gaussian kernel that holds true for integrable solutions of the Heat Equation posed in the Euclidean…
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…
Equivalence between radial solutions of different parabolic gradient-diffusion equations and applications
Mikko Parviainen, Juan Luis Vázquez
We consider a general form of a parabolic equation that generalizes both the standard parabolic -Laplace equation and the normalized version that has been proposed in stochastic…
Porous medium equation with nonlocal pressure
Diana Stan, Félix del Teso, Juan Luis Vázquez
We provide a rather complete description of the results obtained so far on the nonlinear diffusion equation , which describes a flow thr…