Maximum principle and existence of Lp-viscosity solutions for fully nonlinear uniformly elliptic equations with measurable and quadratic terms

Shigeaki Koike, Andrzej Świȩch

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

We study Lp-viscosity solutions of fully nonlinear, second-order, uniformly elliptic partial differential equations (PDE) with measurable terms and quadratic nonlinearity. We present a sufficient condition under which the maximum principle holds for Lp-viscosity solution. We also prove stability and existence results for the equations under consideration.

Original languageEnglish
Pages (from-to)491-509
Number of pages19
JournalNonlinear Differential Equations and Applications
Volume11
Issue number4
DOIs
Publication statusPublished - 2004 Dec 1
Externally publishedYes

Keywords

  • Fully nonlinear equation
  • L-viscosity solution
  • Maximum principle
  • Uniformly elliptic equation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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