6 papers
Gradual smoothing: strong hypercontractivity and logarithmic Sobolev inequalities
Arturo de Pablo, David Lee, Fernando Quirós +1
We study the possibility of a gradual improvement as time progresses of the regularity of solutions to evolution problems of parabolic type driven by Lévy-type operators, not neces…
A nonlinear diffusion equation with reaction localized to the half-line
Raúl Ferreira, Arturo de Pablo
We study the behaviour of the solutions to the quasilinear heat equation with a reaction restricted to a half-line and for , $…
Anisotropic nonlocal diffusion equations with singular forcing
Arturo de Pablo, Fernando Quirós, Ana Rodríguez
We prove existence, uniqueness and regularity of solutions of nonlocal heat equations associated to anisotropic stable diffusion operators. The main features are that the right-han…
Remarks on a nonlinear nonlocal operator in Orlicz spaces
Ernesto Correa, Arturo de Pablo
We study integral operators of the type of the fractional -Laplacian operator, and the properties of the correspondin…
Nonlocal operators of order near zero
Ernesto Correa, Arturo de Pablo
We study Dirichlet forms defined by nonintegrable Lévy kernels whose singularity at the origin can be weaker than that of any fractional Laplacian. We show some properties of the a…
On some Critical Problems for the Fractional Laplacian Operator
B. Barrios, E. Colorado, A. de Pablo +1
We study the effect of lower order perturbations in the existence of positive solutions to the following critical elliptic problem involving the fractional Laplacian: (-Δ)^{α/2}u=λ…