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

Goro Akagi, Kazumasa Suzuki

研究成果: Article査読

10 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)457-471
ページ数15
ジャーナルCalculus of Variations and Partial Differential Equations
31
4
DOI
出版ステータスPublished - 2008 4
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 応用数学

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