Estimate of the gradient of a solution of the Dirichlet problem for Monge-Ampère type equations in a domain with nonsmooth boundary
type: Item
instance of: scholarly article
title: Estimate of the gradient of a solution of the Dirichlet problem for Monge-Ampère type equations in a domain with nonsmooth boundary
zbMATH Open document ID: 0863.35043
DOI: 10.1007/BF02364865
author: S. I. Prokof'eva
published in: Journal of Mathematical Sciences (New York)
publication date: 1997-06-03T00:00:00Z
review text: This paper deals with the Dirichlet problem: \[ F_m(a;u)=f(x,u_x)\quad\text{in }\Omega,\quad u=0\quad\text{on }\partial\Omega,\tag{1} \] where \(\Omega\) is a bounded domain in \(\mathbb{R}^n\), \(n\geq 2\), and \(F_m(a,u)\) is the operator of Monge-Ampère type investigated in \textit{N. M. Ivochkina}, the author and \textit{G. V. Yakunina} [J. Math. Sci., New York 73, No. 6, 663-673 (1995); translation from Probl. Mat. Anal. 13, 89-106 (1992; Zbl 0847.35043)]. The author obtains an estimate for the normal derivative of a viscous solution \(u\) to (1), near \(\partial\Omega\), when \(\partial\Omega\) is of class \(C^0\).
reviewed by: Denise Huet
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35J67
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 58J60
zbMATH DE Number: 916348
zbMATH Keywords: Monge-Ampère type equation
zbMATH Keywords: viscosity solution
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 916348