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On the curvature of some free boundaries in higher dimensions
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-3125-3030
Tokyo Metropolitan University.
2012 (English)In: Analysis and Mathematical Physics, ISSN 1664-2368, E-ISSN 1664-235X, Vol. 2, 247-275 p.Article in journal (Refereed) Published
Abstract [en]

It is known that any subharmonic quadrature domain in two dimensions satisfies a natural inner ball condition, in other words there is a specific upper bound on the curvature of the boundary. This result directly applies to free boundaries appearing in obstacle type problems and in Hele-Shaw flow. In the present paper we make partial progress on the corresponding question in higher dimensions. Specifically, we prove the equivalence between several different ways to formulate the inner ball condition, and we compute the Brouwer degree for a geometrically important mapping related to the Schwarz potential of the boundary. The latter gives in particular a new proof in the two dimensional case.

Place, publisher, year, edition, pages
Springer, 2012. Vol. 2, 247-275 p.
Keyword [en]
Quadrature domain, inner ball condition, Schwarz potential, Brouwer degree
National Category
URN: urn:nbn:se:kth:diva-139040DOI: 10.1007/s13324-012-0032-7ISI: 000209055100003OAI: diva2:682658

QC 20140219

Available from: 2013-12-29 Created: 2013-12-29 Last updated: 2015-06-23Bibliographically approved

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