On a certain degenerate parabolic equation associated with the infinity-Laplacian

Goro Akagi, Kazumasa Suzuki

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The comparison, uniqueness and existence of viscosity solutions to the Cauchy-Dirichlet problem are proved for a degenerate parabolic equation of the form ut = Δu, where Δ denotes the so-called infinity-Laplacian given by Δu = ΣNi,j=1 uxiuxj u xixj. Our proof relies on a coercive regularization of the equation, barrier function arguments and the stability of viscosity solutions.

Original languageEnglish
Pages (from-to)18-27
Number of pages10
JournalDiscrete and Continuous Dynamical Systems- Series A
Issue numberSUPPL.
Publication statusPublished - 2007 Sep 1
Externally publishedYes

Keywords

  • Degenerate parabolic equation
  • Infinity-Laplacian
  • Viscosity solution

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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