On ``balayage inwards'' of charges in \(\mathbb{R}^ n\)
type: Item
instance of: scholarly article
title: On ``balayage inwards'' of charges in \(\mathbb{R}^ n\)
zbMATH Open document ID: 0836.31005
DOI: 10.1007/BF01209087
author: Boris Sternin
author: Victor Shatalov
published in: Mathematical Notes
publication date: 1995-09-12T00:00:00Z
review text: Let \(U^f\) stand for the potential of a given density \(f\) in a domain \(\Omega \subset \mathbb{R}^n\). The problem is to find a distribution \(w\) with compact support in \(\Omega\) such that \(U^f= U^w\) outside \(\Omega\) and such that the support of \(w\) is minimal in some sense. The problem is reduced to the complex analytic Cauchy problem, which is the central problem of the article. It is supposed that the boundary of \(\Omega\) is an algebraic hypersurface in \(\mathbb{R}^n\) and that \(f\) has an analytic continuation to the compactification \(\mathbb{C} P^n\) of \(\mathbb{C}^n\).
Mathematics Subject Classification ID: 31B15
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 795654
zbMATH Keywords: balayage of charges
zbMATH Keywords: complex analytic Cauchy problem
reviewed by: Miroslav Dont
MaRDI profile type: Publication
cites work: Q3812610
cites work: Q3817114
cites work: Q3362551
cites work: Global existence results for linear analytic partial differential equations
cites work: Le calcul différentiel et intégral sur une variété analytique complexe. (Problème de Cauchy. III.)
cites work: Q5599495
description: scientific article; zbMATH DE number 795654