On fully nonlinear PDEs derived from variational problems of Lp norms

Toshihiro Ishibashi, Shigeaki Koike

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

The p-Laplace operator arises in the Euler-Lagrange equation associated with a minimizing problem which contains the Lpnorm of the gradient of functions. However, when we adapt a different Lpnorm equivalent to the standard one in the minimizing problem, a different p-Laplace-type operator appears in the corresponding Euler-Lagrange equation. First, we derive the limit PDE which the limit function of minimizers of those, as p → ∞, satisfies in the viscosity sense. Then we investigate the uniqueness and existence of viscosity solutions of the limit PDE.

Original languageEnglish
Pages (from-to)545-569
Number of pages25
JournalSIAM Journal on Mathematical Analysis
Volume33
Issue number3
DOIs
Publication statusPublished - 2001 Jan 1
Externally publishedYes

Fingerprint

Nonlinear PDE
Lp-norm
Fully Nonlinear
Variational Problem
Euler-Lagrange Equations
Viscosity
P-Laplace Operator
Viscosity Solutions
Laplace
Minimizer
Existence and Uniqueness
Gradient
Operator

Keywords

  • Comparison principle
  • Concave solution
  • Fully nonlinear equation
  • Viscosity solution
  • ∞-Laplacian

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

On fully nonlinear PDEs derived from variational problems of Lp norms. / Ishibashi, Toshihiro; Koike, Shigeaki.

In: SIAM Journal on Mathematical Analysis, Vol. 33, No. 3, 01.01.2001, p. 545-569.

Research output: Contribution to journalArticle

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