The local regularity for strong solutions of the Hessian quotient equation
type: Item
instance of: scholarly article
title: The local regularity for strong solutions of the Hessian quotient equation
zbMATH Open document ID: 1126.35027
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-04-07T00:00:00Z
review text: The authors consider the local \(C^{1,1}\) estimate and the regularity of the strong solutions for the Hessian quotient equation \[ {S_k(D^2 u)\over S_e(D^2 u)}= c,\quad\text{a. e. }x\in\Omega,\;0\leq\ell< k\leq n, \] where \(\Omega\) is a domain in \(\mathbb{R}^n\), \(C\) is a positive constant, \(D^2u\) denotes the Hessian of a function \(u\) in \(\Omega\), and \(S_j(D^2u)\) is denoted to the \(j\)th elementary symmetric function of the eigenvalues \(\lambda= (\lambda_1,\dots, \lambda_n)\) of \(D^2u\). To this end, the authors use the Reilly formula and the Alexander maximum principle. They also extend the regularity result in the special Lagrangian case to the Hessian quotient case.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 2153755
zbMATH Keywords: Hessian equation
zbMATH Keywords: Strong solutions
zbMATH Keywords: Local regularity
author: Shu-Mao Liu
author: Jiguang Bao
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.08.046
OpenAlex ID: W2067869010
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DOI: 10.1016/J.JMAA.2004.08.046
description: scientific article; zbMATH DE number 2153755