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Regularity of a free boundary at the infinity point
KTH, Tidigare Institutioner                               , Matematik.ORCID-id: 0000-0002-1316-7913
2000 (engelsk)Inngår i: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 25, nr 12-Nov, s. 2055-2086Artikkel i tidsskrift (Fagfellevurdert) 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}.

##### sted, utgiver, år, opplag, sider
2000. Vol. 25, nr 12-Nov, s. 2055-2086
##### Emneord [en]
unbounded free boundary, regularity at infinity, cone problem, null quadrature domains, dimensions
##### Identifikatorer
ISI: 000165109800003OAI: oai:DiVA.org:kth-20143DiVA, id: diva2:338836
QC 20100525Tilgjengelig fra: 2010-08-10 Laget: 2010-08-10 Sist oppdatert: 2017-12-12bibliografisk kontrollert

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Shahgholian, Henrik.

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##### Av forfatter/redaktør
Shahgholian, Henrik.
##### I samme tidsskrift
Communications in Partial Differential Equations

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