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An overview of unconstrained free boundary problems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0002-1316-7913
2015 (English)In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 373, no 2050, 20140281Article in journal (Refereed) Published
Abstract [en]

In this paper, we present a survey concerning unconstrained free boundary problems of type F-1(D(2)u, del u, u, x) = 0 in B-1 boolean AND Omega, F-2(D(2)u, del u, u, x) = 0 in B-1 \ Omega, u is an element of S(B-1), where B-1 is the unit ball, Omega is an unknown open set, F-1 and F-2 are elliptic operators (admitting regular solutions), and S is a functions space to be specified in each case. Our main objective is to discuss a unifying approach to the optimal regularity of solutions to the above matching problems, and list several open problems in this direction.

Place, publisher, year, edition, pages
2015. Vol. 373, no 2050, 20140281
Keyword [en]
free boundary problems, obstacle-type, optimal regularity, matching data
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-173962DOI: 10.1098/rsta.2014.0281ISI: 000360825300008Scopus ID: 2-s2.0-84939155428OAI: oai:DiVA.org:kth-173962DiVA: diva2:859257
Funder
Swedish Research Council
Note

QC 20151006

Available from: 2015-10-06 Created: 2015-09-24 Last updated: 2017-12-01Bibliographically approved

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Shahgholian, Henrik

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  • nn-NB
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