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The Case of p-Laplacian Operator

  • Messoud Efendiev
Chapter
Part of the Fields Institute Monographs book series (FIM, volume 36)

Abstract

We are interested in quasilinear elliptic problems over a half-space of the form
$$\displaystyle\left \{ \begin {array}{l}\Delta _p u+f(u)=0 \mbox{ in } \mathbb {R}_+\times \mathbb {R}^{N-1},\\ u(0, x_2,\ldots , x_N)=u_0(x_2,\ldots , x_N), \end {array} \right .$$
and similar problems over a quarter-space
$$\displaystyle\left \{ \begin {array}{l} \Delta _p u+f(u)=0 \mbox{ in } \mathbb {R}_+\times \mathbb {R}^{N-2}\times \mathbb {R}_+,\\ u(0, x_2,\ldots , x_N)=u_0(x_2,\ldots , x_N),\\ u(x_1,x_2,\ldots , x_{N-1}, 0)=0. \end {array} \right .$$

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Copyright information

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Authors and Affiliations

  • Messoud Efendiev
    • 1
  1. 1.Institute of Computational BiologyHelmholtz Center MunichNeuherbergGermany

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