Teoria de fronteira livre para equações não lineares singulares/degeneradas não homogêneas: uma abordagem não variacional

Abstract

Free boundary problems are related to questions involving solutions to partial differential equations. Its applicability extends to several areas of knowledge. Our goal is study the free boundary regularity of the one phase problem to the g-laplacian. Deal with a sofisticate machinery, we get sucess. Getting, the C 1,α regularity to free boundary in two results: the fi rst, heuristically, the free boundary is in between two planes and second, when its has Lipschitz regularity in a neiborhood of point. In this last one, the C 1,α regularity occurs in a smaller (possibly) neighborhood of the point in question. Although the operator is of the divergent form, where we traditionally use a variational approach, we were able to use results that guarantee the equivalence between solutions in the sense of distributions and in the sense of viscosity to proceed with our intentions.