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The fractional Cheeger problem
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-4309-9242
2014 (English)In: Interfaces and free boundaries (Print), ISSN 1463-9963, E-ISSN 1463-9971, Vol. 16, no 3, 419-458 p.Article in journal (Refereed) Published
Abstract [en]

Given an open and bounded set Omega subset of R-N, we consider the problem of minimizing the ratio between the s-perimeter and the N-dimensional Lebesgue measure among subsets of Omega. This is the non-local version of the well-known Cheeger problem. We prove various properties of optimal sets for this problem, as well as some equivalent formulations. In addition, the limiting behaviour of some nonlinear and non-local eigenvalue problems is investigated, in relation with this optimization problem. The presentation is as self-contained as possible.

Place, publisher, year, edition, pages
2014. Vol. 16, no 3, 419-458 p.
Keyword [en]
Cheeger constant, non-local eigenvalue problems, almost minimal surfaces
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-155156DOI: 10.4171/IFB/325ISI: 000342537400005Scopus ID: 2-s2.0-84905001290OAI: oai:DiVA.org:kth-155156DiVA: diva2:760216
Note

QC 20141103

Available from: 2014-11-03 Created: 2014-10-31 Last updated: 2017-12-05Bibliographically approved

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Lindgren, Erik

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