Nonexistence of positive very weak solutions to an elliptic problem with boundary reactions
type: Item
instance of: scholarly article
title: Nonexistence of positive very weak solutions to an elliptic problem with boundary reactions
zbMATH Open document ID: 1309.35016
author: Futoshi Takahashi
published in: Kodai Mathematical Journal
publication date: 2015-01-19T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.kmj/1414674620
full work available at URL: 111F0000020-14-2.pdf
review text: The paper studies positive solutions of the nonlinear Robin problem for the Laplace equation \(\Delta u=0\) in \(\Omega \), \(\partial u/\partial \nu +u=au^p+f\) on \(\partial \Omega \). Here \(\Omega \subset \mathbb{R}^N\), \(N\geq 3\), is a bounded domain with smooth boundary, \(p>1\), \(f\in L^\infty (\partial \Omega )\), \(f\geq 0\), \(f\not \equiv 0\), \(a\in L^1(\partial \Omega )\), \(a\geq 0\). Under assumption that \(0\in \partial \Omega \) and \(\int_{\partial \Omega }a(y) |y|^{2-N}\;ds(y)=\infty \) it is shown that there is no positive solution of the problem even in the very weak sense.
reviewed by: Dagmar Medková
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 35B09
zbMATH DE Number: 6387915
zbMATH Keywords: very weak solution
zbMATH Keywords: boundary reaction
zbMATH Keywords: nonexistence
zbMATH Keywords: positive solutions
zbMATH Keywords: nonlinear Robin problem
zbMATH Keywords: Laplace equation
MaRDI profile type: Publication
OpenAlex ID: W2063672029
DOI: 10.2996/KMJ/1414674620
description: scientific article; zbMATH DE number 6387915