Estimativas de Schauder

Abstract

In this work, we study regularity of solutions of second order PDE’s. More precisely, we study universal C

2,α regularity estimates of solutions, which are also known as Schauder estimates. We divide the thesis in three parts: in the first part, we study results of C

2,α solutions of Poisson Equations which are a-priori α-H ̈older continuous.

In the second part, we study C

2,α regularity of solutions of linear second order elliptic

PDE’s, with C α coefficients, through an interior estimate. Finally, we study the C 2,α regularity of viscosity solutions of fully non-linear second order elliptic PDE’s.