JournalspmVol. 64 , No. 2DOI 10.4171/pm/1780

The influence of domain geometry in the boundary behavior of large solutions of degenerate elliptic problems

  • Michèle Grillot

    Université d'Orléans, France
  • Philippe Grillot

    Université d'Orléans, France
The influence of domain geometry in the boundary behavior of large solutions of degenerate elliptic problems cover

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Abstract

In this paper we study the asymptotic boundary behavior of large solutions of the equation Δu=dαup\Delta u=d^{\alpha}u^p in a regular bounded domain Ω\Omega in RN\R^N, N2N\geq 2, where d(x)d(x) denotes the distance from xx to Ω\partial\Omega, p>1p>1 and α>0\alpha>0. We precise the expansion which depends on the mean curvature of the boundary.