Degenerate Elliptic Problems in a Class of Free Domains

• Autor(a) principal: Rodrigues, José Francisco
• Data de Publicação: 1999
• Outros Autores: Urbano, José Miguel
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10316/4659; https://doi.org/10.1016/S0021-7824(99)00017-3
• topic: p-Laplacian operator; Free boundary problems; Continuous dependence; Unidirectional non-Newtonian flows

We study a mixed boundary value problem for an operator of p-Laplacian type. The main feature of the problem is the fact that the exact domain where it is considered is not known a priori and is to be determined so that a certain integral condition is satisfied. We establish the existence of a unique solution to the problem, by means of the analysis of the range of an appropriate real function, and we show the continuous dependence with respect to a family of operators. These results can be applied to the study of unidirectional non-Newtonian flows of power-law type, in particular to solve a simplified problem arising in theoretical glaciology and to show the existence of a Bingham flow in an open channel; the uniqueness in this case is an open problem.