Existence and Regularity of Solutions: Nonlocal and Nonlinear Models

Abstract

The first words are for my parents Sulma and Fausto who have sacrificed a lot. I am strongly grateful for the support given by them and, above all, my mother's perseverance to overcome the difficulties. I also thank my brothers Kenny, Antony and Claudio. We have worked together to move forward, thank you very much to all of them. I would like to thank my advisors Edgard and Ricardo for the continuous support, for their patience, motivation, and immense knowledge.I also like to thank the rest of my thesis committee for their suggestions and contributions, and for accepting the invitation.My sincere thanks also goes to Creuza and all administrative staff of the Department of Mathematics for helping me to fulfill all the bureaucracy requirements.To my many friends who have supported me throughout the process. I will always appreciate all they have done.This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior -Brasil (CAPES) -Finance Code 001. I also thank PETROBRAS by its financial aid.