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Generalized dirichlet problem in nonlinear potential theory

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Abstract

The operator extending the classical solution of the Dirichlet problem for the quasilinear elliptic equation divA (x,▽u)=0 akin to thep-Laplace equation is shown to be unique providedA obeys a specific order principle. The Keldych lemma is also generalized to this nonlinear setting.

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Authors and Affiliations

  1. Department of Mathematics, University of Jyväskylä, Seminaarinkatu 15, 40100, Jyväskylä, Finland

    Tero Kilpeläinen

  2. Matematicko-fyzykální fakulta, University Karlovy, Sokolovská 83, 186 00, Praha 8, Czechoslovakia

    Jan Malý

Authors
  1. Tero Kilpeläinen
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  2. Jan Malý
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Additional information

Part of this research was performed in 1988–1989 while a visitor at Indiana University, Bloomington, Indiana.

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Kilpeläinen, T., Malý, J. Generalized dirichlet problem in nonlinear potential theory. Manuscripta Math 66, 25–44 (1990). https://doi.org/10.1007/BF02568480

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  • DOI: https://doi.org/10.1007/BF02568480

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