Affiliation:
1. Departamento de Matemática Instituto de Matemática, Estastística e Ciência da Computação Universidade Estadual de Campinas ‐ UNICAMP., Cidade Universitária Zeferino Vaz Campinas SP Brazil
2. Instituto de Matemática e Computaçáo Universidade Federal de Itajubá, Campus Prof. José Rodrigues Seabra Itajubá MG Brazil
3. Departamento de Matemática Universidade Federal do Ceará, Campus do Pici Fortaleza‐CE Brazil
Abstract
AbstractWe establish the existence and sharp global regularity results (, and estimates) for a class of fully nonlinear elliptic Partial Differential Equations (PDEs) with unbalanced variable degeneracy. In a precise way, the degeneracy law of the model switches between two different kinds of degenerate elliptic operators of variable order, according to the null set of a modulating function . The model case in question is given by
for a bounded, regular, and open set , and appropriate continuous data , , and . Such sharp regularity estimates generalize and improve, to some extent, earlier ones via geometric treatments. Our results are consequences of geometric tangential methods and make use of compactness, localized oscillating, and scaling techniques. In the end, our findings are applied in the study of a wide class of nonlinear models.
Funder
Conselho Nacional de Desenvolvimento Científico e Tecnológico
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Cited by
2 articles.
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