Maximum principle for Pucci equations with sublinear growth in \(D u\) and its applications
type: Item
instance of: scholarly article
title: Maximum principle for Pucci equations with sublinear growth in \(D u\) and its applications
zbMATH Open document ID: 1378.35052
author: S. Koike
author: Takahiro Kosugi
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2017-08-03T00:00:00Z
review text: In this paper, the authors study the Dirichlet boundary value problems for Pucci extremal equations with sublinear growth terms in the first derivatives: \[ \mathcal P^{\pm}(D^2u)+\gamma|Du|+\mu|Du|^m=f\text{ in }\Omega \] where \(\Omega\in\mathbb R^n\), \(0<m<1\), and \(\gamma,\mu,f:\Omega\to\mathbb R\) are in \(L^p\) spaces with appropriate powers \(p\). The paper is organized in 5 sections. After an introduction, in Section 1, in Section 2, the authors introduce notations and recall some known results. Section 3 is devoted to showing the existence of \(L^p\)-strong solutions. Using the existence result, the authors show the ABP (Alexandrov-Bakelman-Pucci) maximum principle for \(L^p\)-viscosity solutions. Section 4 is dedicated to Harnack inequality. In Section 5, as an application, the authors show the continuity of viscosity solutions of \(\alpha\)-Poisson type equation for \(1<\alpha<2\).
reviewed by: Cristian Chifu
Mathematics Subject Classification ID: 35B50
Mathematics Subject Classification ID: 35D40
zbMATH DE Number: 6756448
zbMATH Keywords: ABP maximum principle
zbMATH Keywords: weak Harnack inequality
zbMATH Keywords: \(p\)-Laplace operator
zbMATH Keywords: Alexandrov-Bakelman-Pucci
zbMATH Keywords: \(\alpha\)-Poisson type equation
MaRDI profile type: Publication
full work available at URL: j.na.2017.03.018
OpenAlex ID: W2618950295
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DOI: 10.1016/J.NA.2017.03.018
description: scientific article; zbMATH DE number 6756448