Maximum principle for Pucci equations with sublinear growth in Du and its applications

Shigeaki Koike, Takahiro Kosugi

Research output: Contribution to journalArticle

Abstract

It is obtained that there exist strong solutions of Pucci extremal equations with sublinear growth in Du and measurable ingredients. It is proved that a strong maximum principle holds in a local sense in Lemma 4.1 although even the (weak) maximum principle fails. By using this existence result, it is shown that the ABP type maximum principle and the weak Harnack inequality for viscosity solutions hold true. As an application, the Hölder continuity for viscosity solutions of possibly singular, quasilinear equations is established.

Original languageEnglish
Pages (from-to)1-15
Number of pages15
JournalNonlinear Analysis, Theory, Methods and Applications
Volume160
DOIs
Publication statusPublished - 2017 Sep 1
Externally publishedYes

Fingerprint

Maximum principle
Viscosity Solutions
Maximum Principle
Strong Maximum Principle
Harnack Inequality
Quasilinear Equations
Strong Solution
Viscosity
Existence Results
Lemma

Keywords

  • ABP maximum principle
  • p-Laplace operator
  • Weak Harnack inequality

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Maximum principle for Pucci equations with sublinear growth in Du and its applications. / Koike, Shigeaki; Kosugi, Takahiro.

In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 160, 01.09.2017, p. 1-15.

Research output: Contribution to journalArticle

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