Degenerate Elliptic Problems in a Class of Free Domains

• Author(s): Rodrigues, José Francisco ; Urbano, José Miguel
• Date: 1999
• Persistent ID: http://hdl.handle.net/10316/4659
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): p-Laplacian operator; Free boundary problems; Continuous dependence; Unidirectional non-Newtonian flows
• Document Type: Article
• Language: English

Description

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. http://www.sciencedirect.com/science/article/B6VMD-3XG1V0K-3/1/1863148ed1fd455c63598674cb1e9692