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Regularity of free boundaries a heuristic retro
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, 20150209Article, review/survey (Refereed) Published
Abstract [en]

This survey concerns regularity theory of a few free boundary problems that have been developed in the past half a century. Our intention is to bring up different ideas and techniques that constitute the fundamentals of the theory. We shall discuss four different problems, where approaches are somewhat different in each case. Nevertheless, these problems can be divided into two groups: (i) obstacle and thin obstacle problem; (ii) minimal surfaces, and cavitation flow of a perfect fluid. In each case, we shall only discuss the methodology and approaches, giving basic ideas and tools that have been specifically designed and tailored for that particular problem. The survey is kept at a heuristic level with mainly geometric interpretation of the techniques and situations in hand.

Place, publisher, year, edition, pages
2015. Vol. 373, no 2050, 20150209
Keyword [en]
regularity for free boundaries, minimal surfaces, cavitation, obstacle, thin obstacle
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-173960DOI: 10.1098/rsta.2015.0209ISI: 000360825300015Scopus ID: 2-s2.0-84939135284OAI: oai:DiVA.org:kth-173960DiVA: diva2:859263
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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