On fully nonlinear PDEs derived from variational problems of Lp norms

Toshihiro Ishibashi*, Shigeaki Koike

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


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
Issue number3
Publication statusPublished - 2001
Externally publishedYes


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

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics


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