Regularidade Hölder até a fronteira do gradiente de soluções fracas de EDPs singulares/degeneradas em espaços de Orlicz e aplicações a problemas de fronteira livre

Abstract

In this thesis work we discus results that concern the regularity of solutions in the weak sense for elliptical equations of divergent form singular/degenerate. We consider such solutions defined in half-balls. Under the hypothesis of a given boundary C1,α for 0 < α < 1, we show that the solution of a Dirichlet problem of this type has regularity C1,β for some 0 < β ≤ α up to the boundary. We then apply this result to theorems in the context of free boundary problems and combustion and flame propagation problems.