Very weak solutions of Poisson's equation with singular data under Neumann boundary conditions
type: Item
instance of: scholarly article
title: Very weak solutions of Poisson's equation with singular data under Neumann boundary conditions
zbMATH Open document ID: 1314.35025
author: Jochen Merker
author: J.-M. Rakotoson
published in: Calculus of Variations and Partial Differential Equations
publication date: 2015-03-23T00:00:00Z
review text: The authors are concerned with the study of very weak solutions \(u\in L^1(\Omega)\) for the Poisson's equation \(-\Delta u=f\) in \(\Omega\), subject to Neumann boundary conditions. Here \(\Omega\) is a smooth and bounded domain and \(f\) is a singular data. The authors are first concerned with general existence and uniqueness results. Next, the regularity of solutions is discussed.
reviewed by: Marius Ghergu
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35D30
zbMATH DE Number: 6418480
zbMATH Keywords: Poisson's equation
zbMATH Keywords: Neumann boundary condition
zbMATH Keywords: singular data
MaRDI profile type: Publication
full work available at URL: s00526-014-0730-0
OpenAlex ID: W2069864438
Wikidata QID: Q115387391
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DOI: 10.1007/S00526-014-0730-0
description: scientific article; zbMATH DE number 6418480