Solutions to the obstacle problem as Green potentials
type: Item
instance of: scholarly article
title: Solutions to the obstacle problem as Green potentials
zbMATH Open document ID: 0577.49005
DOI: 10.1007/BF02790192
author: Makoto Sakai
published in: Journal d'Analyse Mathématique
publication date: 1985-01-01T00:00:00Z
review text: An obstacle problem is discussed by using a new type of the ''sweeping-out principle'' of measures and the theory due to Cartan and Deny. The first result is a fundamental inequality between measures. The balayage measure \(\mu\) of a solution \(G\mu\) to the obstacle problem with obstacle \(\psi =G\nu_ 1-G\nu_ 2\) satisfies \(\mu \leq \nu_ 1\), where \(G\mu\) is the Green potential of \(\mu\) and \(\nu_ 1\), \(\nu_ 2\) are positive measures with finite Green energy. The second consequence is that quadrature domains with weight are closely related to the complements of the coincident sets in the obstacle problem.
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 31B05
Mathematics Subject Classification ID: 31B35
Mathematics Subject Classification ID: 31B15
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 35J85
zbMATH DE Number: 3923521
zbMATH Keywords: obstacle problem
zbMATH Keywords: balayage measure
zbMATH Keywords: Green potential
zbMATH Keywords: quadrature domains
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3923521