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Gamma limits in some Bernoulli free boundary problem
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1316-7913
2005 (English)In: Archiv der Mathematik, ISSN 0003-889X, E-ISSN 1420-8938, Vol. 84, no 1, 79-87 p.Article in journal (Refereed) Published
Abstract [en]

We study the limit cases p --> infinity and p --> 1 of the functionals (1) E-p(u) := integral(Rn) {1/p(|delu|/a) (p) + p-1/ p chi({u>0})} dx, where u = 1 on a given compact set K subset of R-n, and a > 0 is also given. Minimizers u(p) of these functionals have uniformly bounded support Omega(p) := {u(p) > 0} and satisfy (2) - Delta(p)u(p) = 0 in Omega(p), u(p) = 1 on K, |delu(p)| = a on partial derivativeOmega(p).

Place, publisher, year, edition, pages
2005. Vol. 84, no 1, 79-87 p.
Keyword [en]
viscosity solutions, existence
URN: urn:nbn:se:kth:diva-14434DOI: 10.1007/s00013-004-1334-2ISI: 000225839400008ScopusID: 2-s2.0-12444257806OAI: diva2:332475
QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

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Shahgholian, Henrik.
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