Monatshefte für Mathematik

, 154:303 | Cite as

The obstacle problem for nonlinear elliptic equations with variable growth and L1-data

  • José Francisco Rodrigues
  • Manel Sanchón
  • José Miguel Urbano
Article

Abstract.

The aim of this paper is twofold: to prove, for L1-data, the existence and uniqueness of an entropy solution to the obstacle problem for nonlinear elliptic equations with variable growth, and to show some convergence and stability properties of the corresponding coincidence set. The latter follow from extending the Lewy-Stampacchia inequalities to the general framework of L1.

2000 Mathematics Subject Classification: 35J85, 35J70, 35B30, 35R35 
Key words: Obstacle problem, variable growth, entropy solutions, L1-data, Lewy-Stampacchia inequalities, stability 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • José Francisco Rodrigues
    • 1
    • 2
  • Manel Sanchón
    • 1
  • José Miguel Urbano
    • 1
  1. 1.University of CoimbraCoimbraPortugal
  2. 2.Universidade de LisboaLisboaPortugal

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