Degenerate elliptic problems in a class of free domains

José Francisco Rodrigues, José Miguel Urbano

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2 Scopus citations


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. © Elsevier, Paris.
Original languageEnglish (US)
Pages (from-to)819-840
Number of pages22
JournalJournal des Mathematiques Pures et Appliquees
Issue number8
StatePublished - Jan 1 1999
Externally publishedYes

Bibliographical note

Generated from Scopus record by KAUST IRTS on 2023-02-15

ASJC Scopus subject areas

  • Applied Mathematics
  • General Mathematics


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