A priori bounds and necessary conditions for solvability of prescribed curvature equations
type: Item
instance of: scholarly article
title: A priori bounds and necessary conditions for solvability of prescribed curvature equations
zbMATH Open document ID: 0703.35070
DOI: 10.1007/BF02568424
author: Neil S. Trudinger
published in: Manuscripta Mathematica
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155491
review text: An important estimate for the magnitude of solutions of the prescribed higher order mean curvature equations is proven. The results include well known sharp estimates for the mean and Gauss curvature equations. Sharp existence theorems are thus derived for the Dirichlet problem with the aid of already known first and second order derivative estimates. Attention should also be drawn to certain Poincaré and Sobolev type inequalities which are derived as auxiliary results.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 4152995
zbMATH Keywords: higher order mean curvature equations
zbMATH Keywords: existence
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: Poincaré and Sobolev type inequalities
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4152995