Fiorella Maria Rendón Garcia
Advisor: Boyan Sirakov
Thesis Title: Global boundary weak Harnack inequality for general uniformly elliptic equations in divergence form and applications
Defense: 02/05/2022 | Abstract | Thesis
Depto de Matemática PUC Rio - Prédio Cardeal Leme - Sala 856
In this Ph.D. thesis we give a global extension of the interior weak Harnack inequality for a general class of divergence-type elliptic equations, under very weak regularity assumptions on the differential operator. In this way we generalize and unify all previous results of this type. As an application, we prove a priori estimates for a class of quasilinear elliptic problems with quadratic growth on the gradient and we investigate, under various assumptions, the multiplicity of the solutions obtained for this problem.