Desigualdade de Adams em domínios ilimitados

• Autor(a) principal: Rocha, Fábio Sodré
• Data de Publicação: 2018
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/8859
• topic: Desigualdade de Adams; Crescimento crítico; Desigualdade de Trudinger-Moser; Espaços de Sobolev; Simetrização de Schwarz; Adams inequality; Critical growth; Trudinger-Moser inequality; Sobolev spaces; Schwarz symmetrization; CIENCIAS EXATAS E DA TERRA::MATEMATICA

In this work our aim is to present an extension of the Trudinger-Moser inequality [20] in unbounded domains of Rn for Sobolev Spaces involving high order derivatives. This inequality is nowadays known as Adams-type inequality [1]. We study the techniques developed in the works due to F. Sani and B. Ruf in [23] and due to N. Lam and G. Lu in [16] which are, essentially, combinations of the Comparison Principle of Trombetti and Vazquez for polyharmonic operators and a symmetrization argument, also known as Schwarz Symmetrization. "With such techniques in hands", our aim is to reduce our problem to the radial case and, as a consequence, find an upper bound for the supremum over all functions belonging to the unit ball of Wn;mn (Rn) provided with some specific norm, as well as the sharpness of the constant that appears in Adams inequalities.