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Equilibrium points of a singular cooperative system with free boundary
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1316-7913
2015 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 280, 743-771 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we initiate the study of maps minimising the energy integral(D)(vertical bar del u vertical bar(2) + 2 vertical bar u vertical bar) dx, which, due to Lipschitz character of the integrand, gives rise to the singular Euler equations Delta u = u / vertical bar u vertical bar chi({vertical bar u vertical bar >0}), u = (u(1,) ... ,u(m)) Our primary goal in this paper is to set up a road map for future developments of the theory related to such energy minimising maps. Our results here concern regularity of the solution as well as that of the free boundary. They are achieved by using monotonicity formulas and epiperimetric inequalities, in combination with geometric analysis.

Place, publisher, year, edition, pages
2015. Vol. 280, 743-771 p.
Keyword [en]
Free boundary, Regularity of the singular set, Unique tangent cones, Partial regularity
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-172480DOI: 10.1016/j.aim.2015.04.014ISI: 000357700800024Scopus ID: 2-s2.0-84929376546OAI: oai:DiVA.org:kth-172480DiVA: diva2:848738
Funder
Swedish Research Council
Note

QC 20150826

Available from: 2015-08-26 Created: 2015-08-25 Last updated: 2017-12-04Bibliographically approved

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Shahgholian, Henrik

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