187 citations · 856 across the 36 of their papers we have counts for
42 papers
Anisotropic p-Laplacian Evolution of Fast Diffusion type
Filomena Feo, Juan Luis Vazquez, Bruno Volzone
We study an anisotropic, possibly non-homogeneous version of the evolution -Laplacian equation when fast diffusion holds in all directions. We develop the basic theory and prove…
A simple proof of the generalized Leibniz rule on bounded Euclidean domains
Quoc-Hung Nguyen, Yannick Sire, Juan-Luis Vazquez
This note is devoted to a simple proof of the generalized Leibniz rule in bounded domains. The operators under consideration are the so-called spectral Laplacian and the restricted…
Anisotropic Fast Diffusion Equations
Filomena Feo, Juan Luis Vázquez, Bruno Volzone
We prove the existence of self-similar fundamental solutions (SSF) of the anisotropic porous medium equation in the suitable fast diffusion range. Each of such SSF solutions is uni…
On the two-phase fractional Stefan problem
Félix del Teso, Jørgen Endal, Juan Luis Vázquez
The classical Stefan problem is one of the most studied free boundary problems of evolution type. Recently, there has been interest in treating the corresponding free boundary prob…
The porous medium equation on Riemannian manifolds with negative curvature: the superquadratic case
Gabriele Grillo, Matteo Muratori, Juan Luis Vázquez
We study the long-time behaviour of nonnegative solutions of the Porous Medium Equation posed on Cartan-Hadamard manifolds having very large negative curvature, more precisely when…
Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations
Matteo Bonforte, Alessio Figalli, Juan Luis Vazquez
We investigate quantitative properties of nonnegative solutions to the semilinear diffusion equation , posed in a bounded domain $Ω\subset {\mathbb…