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Regularity properties of a free boundary near contact points with the fixed boundary
KTH, Superseded Departments, Mathematics.ORCID iD: 0000-0002-1316-7913
2003 (English)In: Duke mathematical journal, ISSN 0012-7094, E-ISSN 1547-7398, Vol. 116, no 1, 1-34 p.Article in journal (Refereed) Published
Abstract [en]

In the upper half of the unit ball B+ = {\x\ < 1, x(1) > 0}, let u and Omega (a domain in R-+(n) = {X is an element of R-n : x(1) > 0}) solve the following overdetermined problem: Deltau = chi(Omega) in B+, u = \delu\ = 0 in B+\Omega, u = 0 on Pi boolean AND B, where B is the unit ball with center at the origin, X 0 denotes the characteristic function of Omega, Pi = {x(1) = 0}, n greater than or equal to 2, and the equation is satisfied in the sense of distributions. We show (among other things) that if the origin is a contact point of the free boundary, that is, if u(0) = \delu(0)\ = 0, then partial derivativeOmegaboolean AND Br-0 is the graph of a C-1-function over Pi boolean AND Br-0. The C-1-norm depends on the dimension and sup (B)+ \u\. The result is extended to general subdomains of the unit ball with C-3-boundary.

Place, publisher, year, edition, pages
2003. Vol. 116, no 1, 1-34 p.
Identifiers
URN: urn:nbn:se:kth:diva-22216ISI: 000180683700001OAI: oai:DiVA.org:kth-22216DiVA: diva2:340914
Note
QC 20100525Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved

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Shahgholian, Henrik

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