Two-phase semilinear free boundary problem with a degenerate phase

Handle URI:
http://hdl.handle.net/10754/599853
Title:
Two-phase semilinear free boundary problem with a degenerate phase
Authors:
Matevosyan, Norayr; Petrosyan, Arshak
Abstract:
We study minimizers of the energy functional ∫D[{pipe}∇u{pipe}2 + λ(u+)p]dx for p ∈ (0, 1) without any sign restriction on the function u. The distinguished feature of the problem is the lack of nondegeneracy in the negative phase. The main result states that in dimension two the free boundaries Γ+ = ∂{u > 0} ∩ D andΓ- = ∂{u < 0} ∩ D are C1,α-regular, provided 1 - ∈0 < p < 1. The proof is obtained by a careful iteration of the Harnack inequality to obtain a nontrivial growth estimate in the negative phase, compensating for the apriori unknown nondegeneracy. © 2010 Springer-Verlag.
Citation:
Matevosyan N, Petrosyan A (2010) Two-phase semilinear free boundary problem with a degenerate phase. Calc Var 41: 397–411. Available: http://dx.doi.org/10.1007/s00526-010-0367-6.
Publisher:
Springer Nature
Journal:
Calculus of Variations and Partial Differential Equations
KAUST Grant Number:
KUK-I1-007-43
Issue Date:
16-Oct-2010
DOI:
10.1007/s00526-010-0367-6
Type:
Article
ISSN:
0944-2669; 1432-0835
Sponsors:
We would like to thank the anonymous referee for valuable comments that have contributed to the improvement of the paper. N. Matevosyan is partially supported by the WWTF (Wiener Wissenschafts, Forschungs und Technologiefonds) project No. CI06 003 and by award No. KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST). A. Petrosyan is supported in part by NSF grant DMS-0701015.
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Full metadata record

DC FieldValue Language
dc.contributor.authorMatevosyan, Norayren
dc.contributor.authorPetrosyan, Arshaken
dc.date.accessioned2016-02-28T06:42:55Zen
dc.date.available2016-02-28T06:42:55Zen
dc.date.issued2010-10-16en
dc.identifier.citationMatevosyan N, Petrosyan A (2010) Two-phase semilinear free boundary problem with a degenerate phase. Calc Var 41: 397–411. Available: http://dx.doi.org/10.1007/s00526-010-0367-6.en
dc.identifier.issn0944-2669en
dc.identifier.issn1432-0835en
dc.identifier.doi10.1007/s00526-010-0367-6en
dc.identifier.urihttp://hdl.handle.net/10754/599853en
dc.description.abstractWe study minimizers of the energy functional ∫D[{pipe}∇u{pipe}2 + λ(u+)p]dx for p ∈ (0, 1) without any sign restriction on the function u. The distinguished feature of the problem is the lack of nondegeneracy in the negative phase. The main result states that in dimension two the free boundaries Γ+ = ∂{u > 0} ∩ D andΓ- = ∂{u < 0} ∩ D are C1,α-regular, provided 1 - ∈0 < p < 1. The proof is obtained by a careful iteration of the Harnack inequality to obtain a nontrivial growth estimate in the negative phase, compensating for the apriori unknown nondegeneracy. © 2010 Springer-Verlag.en
dc.description.sponsorshipWe would like to thank the anonymous referee for valuable comments that have contributed to the improvement of the paper. N. Matevosyan is partially supported by the WWTF (Wiener Wissenschafts, Forschungs und Technologiefonds) project No. CI06 003 and by award No. KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST). A. Petrosyan is supported in part by NSF grant DMS-0701015.en
dc.publisherSpringer Natureen
dc.titleTwo-phase semilinear free boundary problem with a degenerate phaseen
dc.typeArticleen
dc.identifier.journalCalculus of Variations and Partial Differential Equationsen
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdomen
dc.contributor.institutionPurdue University, West Lafayette, United Statesen
kaust.grant.numberKUK-I1-007-43en
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