2 papers
math.AP2020
A sufficient condition for asymptotic stability of kinks in general (1+1)-scalar field models
Michał Kowalczyk, Yvan Martel, Claudio Muñoz +1
We study stability properties of kinks for the (1+1)-dimensional nonlinear scalar field theory models \begin{equation*} \partial_t^2ϕ-\partial_x^2ϕ+ W'(ϕ) = 0, \quad (t,x)\in\mathb…
math-ph2018
Existence and non-existence of minimizers for Poincaré-Sobolev inequalities
Rafael D. Benguria, Cristóbal Vallejos, Hanne Van Den Bosch
In this paper we study the existence and non-existence of minimizers for a type of (critical) Poincaré-Sobolev inequalities. We show that minimizers do exist for smooth domains in…