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Viscosity solutions of the p-Laplace equation with nonlinear source

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Abstract.

In the present paper we consider the Dirichlet problem in a convex domain for the multidimensional p-Laplace equation with nonlinear source. We prove the existence of the unique continuous viscosity solution under quite general assumptions on the structure of the source.

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Authors and Affiliations

  1. Department of Mathematics, University of Crete, 71409, Heraklion-Crete, Greece

    Alkis S. Tersenov

  2. Department of Telecommunications Sciences and Technology, University of Peloponesse, 22 100, Tripolis, Greece

    Aris S. Tersenov

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  1. Alkis S. Tersenov
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  2. Aris S. Tersenov
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Correspondence to Alkis S. Tersenov.

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Received: 18 January 2006

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Tersenov, A.S., Tersenov, A.S. Viscosity solutions of the p-Laplace equation with nonlinear source. Arch. Math. 88, 259–268 (2007). https://doi.org/10.1007/s00013-006-1873-9

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  • DOI: https://doi.org/10.1007/s00013-006-1873-9

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