Extension of Díaz-Saá's inequality in \(\mathbb{R}^N\) and application to a system of \(p\)-Laplacian.
type: Item
instance of: scholarly article
title: Extension of Díaz-Saá's inequality in \(\mathbb{R}^N\) and application to a system of \(p\)-Laplacian.
zbMATH Open document ID: 1163.35392
DOI: 10.5565/PUBLMAT_46202_09
published in: Publicacions Matemàtiques
publication date: 2003-06-18T00:00:00Z
review text: The goal of this paper is to extend the Díaz-Saá inequality for the unbounded domain as \(\mathbb R^N\): \[ \int_{\mathbb R^N} \bigg( \frac{-\Delta_pu}{u^{p-1}}+ \frac{\Delta_pv}{v^{p-1}}\bigg) (u^p-v^p)\,dx\geq 0, \] with \(\Delta_pu= \operatorname{div}(|\nabla u|^{p-2}\nabla u)\). To this end the author uses so-called Picone's identity which is very useful in problems involving \(p\)-Laplacian. Moreover, the author studies some properties of the first eigenvalue for a system of \(p\)-Laplacian. Finally, the author uses Díaz-Saá's inequality to prove uniqueness and Egorov's theorem for the isolation.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35P30
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 1876881
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: Díaz-Saá's inequality
zbMATH Keywords: Picone's identity
zbMATH Keywords: Egorov's theorem
author: Karim Chaib
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: publmat 46202 09
OpenAlex ID: W1980280741
description: scientific article; zbMATH DE number 1876881