Solvability of boundary-value problems and criteria for a minimum of integral functionals
type: Item
instance of: scholarly article
title: Solvability of boundary-value problems and criteria for a minimum of integral functionals
zbMATH Open document ID: 0589.49001
DOI: 10.1007/BF01055943
author: N. A. Bobylev
published in: Ukrainian Mathematical Journal
publication date: 1985-01-01T00:00:00Z
review text: The author considers the functional (1) \(F(u)=\int_{\Omega}f(x,u,u_ x)dx\), \(u|_{\partial \Omega}=0\) and the associated Dirichlet problem for the Euler equation (2) \(\sum^{n}_{i=1}df_{p_ i}/dx_ i-f_ u=0\), \(u|_{\partial \Omega}=0\). It is shown that under some circumstances the solution u of (2) is a weak (or) strong local minimum for (1). Applications to variational problems are given.
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35D10
zbMATH DE Number: 3946996
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: Euler equation
zbMATH Keywords: local minimum
reviewed by: Gheorghe Aniculăesei
MaRDI profile type: Publication
cites work: Q4049449
cites work: Q5768796
cites work: Q5552356
full work available at URL: https://doi.org/10.1007/bf01055943
OpenAlex ID: W2026605723
description: scientific article; zbMATH DE number 3946996