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Annali di Matematica Pura ed Applicata

, Volume 178, Issue 1, pp 195–224 | Cite as

Continuous solutions for a degenerate free boundary problem

  • José Miguel Urbano
Article

Abstract

We prove existence of continuous solutions for
$$\partial _t [\gamma \left( \theta \right)] - div(\left| {\nabla \theta } \right|^{p - 2} \nabla \theta ) \ni 0, p > 2$$
, where γ is a maximal monotone graph, by showing equicontinuity of a sequence of approximate solutions. Relations of this type are models for certain free boundary problems like the Stefan problem with nonlinear diffusion.

19991 Mathematics Subject Classification

35D10 35K65 35R35 

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Copyright information

© Fondazione Annali di Matematica Pure ed Applicata 2000

Authors and Affiliations

  • José Miguel Urbano
    • 1
  1. 1.Departamento de Matemática da Universidade de CoimbraCoimbraPortugal

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