Universität zu Köln

Daners, Daniel ORCID: 0000-0002-0122-3789 and Kawohl, Bernd (2010). An isoperimetric inequality related to a Bernoulli problem. Calc. Var. Partial Differ. Equ., 39 (3-4). S. 547 - 556. NEW YORK: SPRINGER. ISSN 0944-2669

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Abstract

Given a bounded domain Omega we look at the minimal parameter I >(Omega) for which a Bernoulli free boundary value problem for the p-Laplacian has a solution minimising an energy functional. We show that amongst all domains of equal volume I >(Omega) is minimal for the ball. Moreover, we show that the inequality is sharp with essentially only the ball minimising I >(Omega). This resolves a problem related to a question asked in Flucher et al. (Reine Angew Math 486:165-204, 1997).

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Daners, Daniel UNSPECIFIED orcid.org/0000-0002-0122-3789 UNSPECIFIED Kawohl, Bernd UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-493039
DOI:	10.1007/s00526-010-0324-4
Journal or Publication Title:	Calc. Var. Partial Differ. Equ.
Volume:	39
Number:	3-4
Page Range:	S. 547 - 556
Date:	2010
Publisher:	SPRINGER
Place of Publication:	NEW YORK
ISSN:	0944-2669
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language FREE-BOUNDARY PROBLEM; MINIMUM PROBLEM; EXISTENCE; OPERATOR Multiple languages Mathematics, Applied; Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/49303