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8 papers · 2 filters
Stability issues in the quasineutral limit of the one-dimensional Vlasov-Poisson equation
Daniel Han-Kwan, Maxime Hauray
This work is concerned with the quasineutral limit of the one-dimensional Vlasov-Poisson equation, for initial data close to stationary homogeneous profiles. Our objective is three…
Local analysis of solutions of fractional semi-linear elliptic equations with isolated singularities
Luis Caffarelli, Tianling Jin, Yannick Sire +1
In this paper, we study the local behaviors of nonnegative local solutions of fractional order semi-linear equations with an isolated singularity, w…
On the nonlocal Fisher-KPP equation: steady states, spreading speed and global bounds
Francois Hamel, Lenya Ryzhik
We consider the Fisher-KPP equation with a non-local interaction term. We establish a condition on the interaction that allows for existence of non-constant periodic solutions, and…
On a fractional Ginzburg-Landau equation and 1/2-harmonic maps into spheres
Vincent Millot, Yannick Sire
This paper is devoted to the asymptotic analysis of a fractional version of the Ginzburg-Landau equation in bounded domains, where the Laplacian is replaced by an integro-different…
Faber-Krahn inequalities in sharp quantitative form
Lorenzo Brasco, Guido De Philippis, Bozhidar Velichkov
The classical Faber-Krahn inequality asserts that balls (uniquely) minimize the first eigenvalue of the Dirichlet-Laplacian among sets with given volume. In this paper we prove a s…
Random homogenisation of a highly oscillatory singular potential
Martin Hairer, Etienne Pardoux, Andrey Piatnitski
In this article, we consider the problem of homogenising the linear heat equation perturbed by a rapidly oscillating random potential. We consider the situation where the space-tim…