Atingibilidade de supremos do tipo Trudinger-Moser e problemas do tipo Henón relacionados

Author(s)

José Vitor Pena

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2020-03-26

Examining board members

Djairo Guedes de Figueiredo; Ademir Pastor Ferreira; Ederson Moreira Dos Santos; João Marcos Bezerra do Ó; Francisco Odair Vieira de Paiva

• Advisor: Djairo Guedes de Figueiredo

Abstract

On this thesis we present some results regarding critical nonlinearities of exponential type with appropriate weights: first regarding the attainability of supremums of Trudinger-Moser and Trudinger-Moser-Hardy-type functionals on the unit ball and on a simply connected domain with $C^1$ boundary containing the origin respectively (both in $\mathbb{R}^2$), and then an existence result for the critical case of an elliptical Dirichlet-type problem with exponential nonlinearity on the unit ball in $\mathbb{R}^2$. We arrive on decay conditions for the limit of the weight at the origin (thus, we do care about the behavior of the weight only on a neighbourhood of the origin, ignoring it on the rest of the domain). This is achieved using Concentration-Compactness-type techniques (AU)

• FAPESP's process: 16/15887-9 - Aspects of Nonlinear Elliptic Equations and Systems
• Grantee: José Vitor Pena
• Support Opportunities: Scholarships in Brazil - Doctorate