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Regularity of a free boundary at the infinity point
KTH, Superseded Departments, Mathematics.ORCID iD: 0000-0002-1316-7913
2000 (English)In: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 25, no 12-Nov, 2055-2086 p.Article in journal (Refereed) Published
Abstract [en]

Suppose there is a nonnegative function u and an open set Ohm subset of R-n(n greater than or equal to 3), satisfying Deltau = chi (Ohm) in B-r(e), u = \delu\ = 0 on B-r(e)\Ohm, where B-r(e) = {x : \x\ > r}. Under a certain thickness condition on R-n\Ohm, we prove that the boundary of {x:x/\x\(2) is an element of Ohm} is a graph of a C-1 function in a neighborhood of the origin. As a by-product of the method of the proof, we also obtain the following result: Replace chi (Ohm) by f chi (Ohm), with a certain assumptions on f. Then for any solution u which is asymptotically nonnegative at infinity, there holds lim(r-->infinity) (\Br\)/(\Ohm boolean AND Br\) is an element of {1/2,1}.

Place, publisher, year, edition, pages
2000. Vol. 25, no 12-Nov, 2055-2086 p.
Keyword [en]
unbounded free boundary, regularity at infinity, cone problem, null quadrature domains, dimensions
URN: urn:nbn:se:kth:diva-20143ISI: 000165109800003OAI: diva2:338836
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

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