Mínimos locais de funcionais com dependência especial via Γ-convergência: com e sem vínculo

Abstract

We address the question of existence of stationary stable solutions to a class of reaction-diffusion equations with spatial dependence in 2 and 3-dimensional bounded domains. The approach consists of proving the existence of local minimizer of the corresponding energy functional. For existence, it was enough to give sufficient conditions on the diffusion coefficient and on the reaction term to ensure the existence of isolated minima of the Γ-limit functional of the energy functional family. In the second part we take the techniques developed in the first part to minimize functional in 2 and 3-dimensional rectangles, with and without constraint, solving in a more general form this problem, which was originaly proposed in 1989 by Robert Kohn and Peter Sternberg.