Existence and uniqueness of viscosity solutions for a degenerate parabolic equation associated with the infinity-Laplacian

Goro Akagi, Kazumasa Suzuki

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

The existence, uniqueness and regularity of viscosity solutions to the Cauchy-Dirichlet problem are proved for a degenerate nonlinear parabolic equation of the form ut =Δ∞u, where Δ∞ denotes the so-called infinity-Laplacian given by Δ∞u = 〈D2uDu, Du〉. To do so, a coercive regularization of the equation is introduced and barrier function arguments are also employed to verify the equi-continuity of approximate solutions. Furthermore, the Cauchy problem is also studied by using the preceding results on the Cauchy-Dirichlet problem.

Original languageEnglish
Pages (from-to)457-471
Number of pages15
JournalCalculus of Variations and Partial Differential Equations
Volume31
Issue number4
DOIs
Publication statusPublished - 2008 Apr 1
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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