Desigualdade de Adams em domínios ilimitados
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Data
2018-08-10
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Universidade Federal de Goiás
Resumo
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.
Descrição
Citação
ROCHA, F. S. Desigualdade de Adams em domínios ilimitados. 2018. 86 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2018.