\(H^1 \cap L^p\) versus \(C^1\) local minimizers
type: Item
instance of: scholarly article
title: \(H^1 \cap L^p\) versus \(C^1\) local minimizers
zbMATH Open document ID: 1474.49002
DOI: 10.1155/2014/646145
author: Yansheng Zhong
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We show that a local minimizer of \(\Phi\) in the \(C^1\) topology must be a local minimizer in the \(H^1 \cap L^p\) topology, under suitable assumptions for the functional \(\Phi=(1/2)\int_\Omega |\nabla u|^2+(1/p)\int_ \Omega |u|^p-\int_\Omega F(x,u)\) with supercritical exponent \(p>2^*=2n/(n-2)\). This result can be used to establish a solution to the corresponding equation admitting sub- and supersolution. Hence, we extend the conclusion proved by \textit{H. Brézis} and \textit{L. Nirenberg} [C. R. Acad. Sci., Paris, Sér. I 317, No. 5, 465--472 (1993; Zbl 0803.35029)], the subcritical and critical case.
Mathematics Subject Classification ID: 49J10
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 7022818
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/646145
OpenAlex ID: W2490488102
Wikidata QID: Q59040332
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description: scientific article; zbMATH DE number 7022818