Sobre a existência de domínios não triviais para o problema sobredeterminado de Serrin em S^n X lR

Abstract

In this work we study the existence of non-trivial domains in $\mathbb{S}^N\times\mathbb{R},$ $N\ge2$, in which there is a solution to Serrin's overdetermined problem, applying the bifurcation theory of solutions. We begin by displaying some prerequisites for which this theory imposes and establishing some concepts and notations. Furthermore, for the completeness of the topic, we introduce the space of Hölder functions, which are widely used. Finally, we present the appropriate techniques to conclude the result that guarantees the existence of solutions to the aforementioned problem.