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4 papers · 2 filters
Compact Sobolev embeddings and torsion functions
Lorenzo Brasco, Berardo Ruffini
For a general open set, we characterize the compactness of the embedding in terms of the summability of its torsion function. In particular, for $1\l…
Hölder regularity for hypoelliptic kinetic equations with rough diffusion coefficients
François Golse, Alexis Vasseur
This paper is dedicated to the application of the DeGiorgi-Nash-Moser regularity theory to the kinetic Fokker-Planck equation. This equation is hypoelliptic. It is parabolic only i…
A double large deviation principle for monge-ampere gravitation
Yann Brenier
Monge-Ampere gravitation is a nonlinear modification of classical Newtonian gravitation, when the Monge-Ampere equation substitutes for the Poisson equation. We establish, through…
Localization for the Schrödinger equation in a locally periodic medium
Grégoire Allaire, Mariapia Palombaro
We study the homogenization of a Schrödinger equation in a locally periodic medium. For the time and space scaling of semi-classical analysis we consider well-prepared initial data…