Nonvariational singular elliptic and parabolic equations

• Autor(a) principal: Sá, Ginaldo de Santana
• Data de Publicação: 2023
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UFPB
• Texto Completo: https://repositorio.ufpb.br/jspui/handle/123456789/26682
• topic: Equações diferenciais parciais; Regularidade de soluções; Equações degeneradas; Equações parabólicas; Partial differential equations; Regularity of solutions; Degenerate equations; Parabolic PDEs; problemas de fronteira livre; EDPs singulares; Free boundary problems; Singular PDEs; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

In this thesis, we develop geometric and analytic approaches for singular partial differential equations governed by fully nonlinear operators. First, we consider elliptic models ruled by the infinity Laplacian. We prove existence, optimal regularity for solutions along the free boundary, nondegeneracy estimates, and fine geometric measure estimates for the free boundary. In the second topic, we study models governed by fully nonlinear uniformly parabolic operators. We obtain existence of solutions, and sharp regularity estimates in space and time. Our arguments are based on a intrinsic perturbation method, Ishii-Lions techniques, and geometric tangential analysis.