Teoria de regularidade para soluções de equações elípticas não-locais - Sobral, Aelson Oliveira (2020)
In this dissertation, our goal is to present a brief introduction to the regularity theory for solution of Nonlocal Elliptic equations. The work is divided in three chapters where we discuss three big papers from Caffarelli and Silvestre. The ideia is to present the Nonlocal version of the existing theory to Uniformly Elliptic operators and we bring important results like an ABP estimate, a comparison principle, Ca and C 1,a Hölder estimates, regularity results by approximation and a version of the Evans-Krylov theorem for solutions of an Integro-Differential equation for which the associated operator is concave.