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Recent Trends in Free Boundary Regularity
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0002-1316-7913
2018 (English)In: GEOMETRY OF PDES AND RELATED PROBLEMS / [ed] Bianchini, C Henrot, A Magnanini, R, SPRINGER INTERNATIONAL PUBLISHING AG , 2018, p. 147-196Chapter in book (Refereed)
Abstract [en]

In this lecture note I shall describe some recent developments of free boundary value problems and their regularity theory. Starting with the classical obstacle problem, and its development along with detailed proofs of each step of the theory, I shall go on to introduce various closely related semi-classical problems. The latter includes Bernoulli type FBP, Semi-and Quasi-linear PDEs with FB, Non-variational FB, and Non-local problems. As the techniques for treating the classical obstacle problem substantially differs from the others we have chosen to only discuss these problems from a heuristic point of view, and focus on approaches and the difficulties of these problems.

Place, publisher, year, edition, pages
SPRINGER INTERNATIONAL PUBLISHING AG , 2018. p. 147-196
Series
Lecture Notes in Mathematics, ISSN 0075-8434 ; 2220
National Category
Computer and Information Sciences
Identifiers
URN: urn:nbn:se:kth:diva-245021DOI: 10.1007/978-3-319-95186-7_5ISI: 000458495800006Scopus ID: 2-s2.0-85054518578ISBN: 978-3-319-95186-7 (print)OAI: oai:DiVA.org:kth-245021DiVA, id: diva2:1293510
Note

QC 20190305

Available from: 2019-03-05 Created: 2019-03-05 Last updated: 2019-03-05Bibliographically approved

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Shahgholian, Henrik

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