Dirichlet problems for general Monge-Ampère equations
type: Item
instance of: scholarly article
title: Dirichlet problems for general Monge-Ampère equations
zbMATH Open document ID: 0771.35020
DOI: 10.1007/BF02570835
published in: Mathematische Zeitschrift
publication date: 1992-08-03T00:00:00Z
full work available at URL: https://eudml.org/doc/174365
review text: The present paper is concerned with boundary value problems for a class of general Monge-Ampère equations \(\text{det}(\nabla^ 2 z)=K(x)f(x,z,\nabla z)\) in \(Q\) with constant Dirichlet data on \(\partial\Omega\) where \(f\) is a positive function and \(K\) non-negative and \(\nabla^ 2 z\) denotes the Hessian of \(z\) with respect to a given metric \(ds^ 2\). A result about existence of solutions in \(C^ \infty(\Omega)\) and some applications to differential geometry are given.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 32W20
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 39986
zbMATH Keywords: smooth geodesic convex solution
author: Jiaxing Hong
MaRDI profile type: Publication
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OpenAlex ID: W2067004289
description: scientific article; zbMATH DE number 39986