A Tour on p(x)-Laplacian Problems When p = ∞

Yiannis Karagiorgos () and Nikos Yannakakis ()
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Yiannis Karagiorgos: National Technical University of Athens
Nikos Yannakakis: National Technical University of Athens

A chapter in Mathematical Analysis, Approximation Theory and Their Applications, 2016, pp 339-361 from Springer

Abstract: Abstract Most of the times, in problems where the p(x)-Laplacian is involved, the variable exponent p(⋅ ) is assumed to be bounded. The main reason for this is to be able to apply standard variational methods. The aim of this paper is to present the work that has been done so far, in problems where the variable exponent p(⋅ ) equals infinity in some part of the domain. In this case the infinity Laplace operator arises naturally and the notion of weak solution does not apply in the part where p(⋅ ) becomes infinite. Thus the notion of viscosity solution enters into the picture. We study both the Dirichlet and the Neumann case.

Keywords: p(x)-Laplacian; Viscosity solution; Infinity harmonic function; Dirichlet problem; Neumann problem; Lipschitz constant (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-31281-1_15

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DOI: 10.1007/978-3-319-31281-1_15

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