Some properties of solutions to a class of Dirichlet boundary value problems
type: Item
instance of: scholarly article
title: Some properties of solutions to a class of Dirichlet boundary value problems
zbMATH Open document ID: 1261.35030
DOI: 10.1155/2012/268612
author: Gejun Bao
author: Tingting Wang
published in: Abstract and Applied Analysis
publication date: 2013-02-04T00:00:00Z
review text: Summary: This paper deals with the following Dirichlet problem: \(d^\ast A(x, g + du) = d^\ast h\) in \(\Omega \subset \mathbb R^n\) on \(\partial \Omega\). Based on its solvability, we derive some properties of its solutions. We mainly get three results. Firstly, we establish an integral estimate for the solutions of the above Dirichlet boundary value problem. Secondly, a stability result of solutions for varying differential forms \(g\) and \(h\) is obtained. Lastly, we present a weak reverse Hölder inequality for solutions.
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35B30
zbMATH DE Number: 6134050
zbMATH Keywords: \(A\)-harmonic equation
zbMATH Keywords: integral estimate
zbMATH Keywords: weak reverse Hölder inequality
Wikidata QID: Q58696192
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/268612
OpenAlex ID: W2038781473
cites work: Nonlinear elliptic boundary value problems
cites work: Nonlinear Hodge theory on manifolds with boundary
cites work: Integral estimates for null Lagrangians
cites work: The p-Harmonic transform beyond its natural domain of definition
cites work: On weakly A-harmonic tensors
cites work: Isoperimetric type inequalities for differential forms on manifolds
cites work: Local and global norm comparison theorems for solutions to the nonhomogeneous A-harmonic equation
cites work: \(p\)-harmonic tensors and quasiregular mappings
cites work: Inequalities for Differential Forms
cites work: Geometric function theory and nonlinear analysis
description: scientific article; zbMATH DE number 6134050