JournalsjemsVol. 12, No. 1pp. 249–277

Anomalous large-time behaviour of the pp-Laplacian flow in an exterior domain in low dimension

  • Juan Luis Vázquez

    Universidad Autónoma de Madrid, Spain
  • Razvan Gabriel Iagar

    Universidad Autónoma de Madrid, Spain
Anomalous large-time behaviour of the $p$-Laplacian flow in an exterior domain in low dimension cover
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Abstract

We study the large time behaviour of weak nonnegative solutions of the p-Laplace equation posed in an exterior domain in space dimension N < p with boundary conditions u = 0. The description is done in terms of matched asymptotics: the outer asymptotic profile is a dipole-like self-similar solution with a singularity at x = 0 and anomalous similarity exponents. The inner asymptotic behaviour is given by a separate-variable profile. We gather both estimates in a global approximant and we also study the behaviour of the free boundary for compactly supported solutions. We complete in this way the analysis made in a previous work for high space dimensions Np, a range in which the large-time influence of the holes is less dramatic.

Cite this article

Juan Luis Vázquez, Razvan Gabriel Iagar, Anomalous large-time behaviour of the pp-Laplacian flow in an exterior domain in low dimension. J. Eur. Math. Soc. 12 (2010), no. 1, pp. 249–277

DOI 10.4171/JEMS/197