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

In: Mathematical Analysis, Approximation Theory and Their Applications

Author

Listed:
  • Yiannis Karagiorgos

    (National Technical University of Athens)

  • Nikos Yannakakis

    (National Technical University of Athens)

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.

Suggested Citation

  • Yiannis Karagiorgos & Nikos Yannakakis, 2016. "A Tour on p(x)-Laplacian Problems When p = ∞," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Vijay Gupta (ed.), Mathematical Analysis, Approximation Theory and Their Applications, pages 339-361, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-31281-1_15
    DOI: 10.1007/978-3-319-31281-1_15
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