A family of nonlinear resolvents
type: Item
instance of: scholarly article
title: A family of nonlinear resolvents
zbMATH Open document ID: 1089.31007
author: Corneliu Udrea
published in: Southeast Asian Bulletin of Mathematics
publication date: 2006-02-22T00:00:00Z
review text: Let \(U\subset \mathbb{R}^k\) be a nonvoid, open, bounded and strictly convex set. With each continuous function on \(\partial U\), the author associates a nonlinear resolvent, corresponding to the non-homogeneous Dirichlet problem for the Monge-Ampère equation. The resolvent consists of increasing operators on \(L^{\infty }(U)\). This sharpens and extends previous results of the author [Rev. Roum. Math. Pures Appl. 40, No. 7-8, 691--710 (1995; Zbl 0869.31014) and ibid. 46, No. 1, 125--136 (2001; Zbl 1046.35036)]. The treatement is carried out in the spirit of \textit{C. Dellacherie} [Potential theory, Proc. Int. Conf., Nagoya/Jap. 1990, 25--32 (1992; Zbl 0762.31005)].
reviewed by: Liliana Popa
Mathematics Subject Classification ID: 31C45
Mathematics Subject Classification ID: 31B35
Mathematics Subject Classification ID: 47H50
zbMATH DE Number: 5008871
zbMATH Keywords: nonlinear operator
zbMATH Keywords: nonlinear resolvents
zbMATH Keywords: maximum principle
zbMATH Keywords: non-homogeneous Dirichlet problem
zbMATH Keywords: strictly convex set
zbMATH Keywords: nonlinear resolvent
zbMATH Keywords: Monge-Ampère equation
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5008871