ASYMPTOTIC BEHAVIOR OF THE FREE INTERFACE FOR ENTIRE VECTOR MINIMIZERS IN PHASE TRANSITIONS

We study globally bounded entire minimizers u : Rn → Rm of Allen-Cahn systems for potentials W ≥ 0 with {W = 0}= {a1, ..., aN } and W (u) ∼ |u− ai|α near u = ai, 0 < α < 2. Such solutions are, over large regions, identically equal to some zeroes of the potential ai’s. We establish the estimate...

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Detalles Bibliográficos
Autores: Alikakos, N., Geng, Z., Zarnescu, A.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2021
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/1996
Acceso en línea:http://hdl.handle.net/20.500.11824/1996
Access Level:acceso abierto
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spelling ASYMPTOTIC BEHAVIOR OF THE FREE INTERFACE FOR ENTIRE VECTOR MINIMIZERS IN PHASE TRANSITIONSAlikakos, N.Geng, Z.Zarnescu, A.We study globally bounded entire minimizers u : Rn → Rm of Allen-Cahn systems for potentials W ≥ 0 with {W = 0}= {a1, ..., aN } and W (u) ∼ |u− ai|α near u = ai, 0 < α < 2. Such solutions are, over large regions, identically equal to some zeroes of the potential ai’s. We establish the estimates Ln(I0 ∩ Br (x0)) ≤ c1r n−1 , Hn−1(∂∗I0 ∩ Br (x0)) ≥ c2r n−1 , r ≥ r0(x0) for the diffuse interface I0 := {x ∈ Rn : min1≤i≤N |u(x)− ai | > 0} and the free boundary ∂I0. Furthermore, if α = 1 we establish the upper bound Hn−1(∂∗I0 ∩ Br (x0)) ≤ c3r n−1 , r ≥ r0(x0).202520252021info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/1996reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)InglésReconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/19962026-06-19T12:47:47Z
dc.title.none.fl_str_mv ASYMPTOTIC BEHAVIOR OF THE FREE INTERFACE FOR ENTIRE VECTOR MINIMIZERS IN PHASE TRANSITIONS
title ASYMPTOTIC BEHAVIOR OF THE FREE INTERFACE FOR ENTIRE VECTOR MINIMIZERS IN PHASE TRANSITIONS
spellingShingle ASYMPTOTIC BEHAVIOR OF THE FREE INTERFACE FOR ENTIRE VECTOR MINIMIZERS IN PHASE TRANSITIONS
Alikakos, N.
title_short ASYMPTOTIC BEHAVIOR OF THE FREE INTERFACE FOR ENTIRE VECTOR MINIMIZERS IN PHASE TRANSITIONS
title_full ASYMPTOTIC BEHAVIOR OF THE FREE INTERFACE FOR ENTIRE VECTOR MINIMIZERS IN PHASE TRANSITIONS
title_fullStr ASYMPTOTIC BEHAVIOR OF THE FREE INTERFACE FOR ENTIRE VECTOR MINIMIZERS IN PHASE TRANSITIONS
title_full_unstemmed ASYMPTOTIC BEHAVIOR OF THE FREE INTERFACE FOR ENTIRE VECTOR MINIMIZERS IN PHASE TRANSITIONS
title_sort ASYMPTOTIC BEHAVIOR OF THE FREE INTERFACE FOR ENTIRE VECTOR MINIMIZERS IN PHASE TRANSITIONS
dc.creator.none.fl_str_mv Alikakos, N.
Geng, Z.
Zarnescu, A.
author Alikakos, N.
author_facet Alikakos, N.
Geng, Z.
Zarnescu, A.
author_role author
author2 Geng, Z.
Zarnescu, A.
author2_role author
author
description We study globally bounded entire minimizers u : Rn → Rm of Allen-Cahn systems for potentials W ≥ 0 with {W = 0}= {a1, ..., aN } and W (u) ∼ |u− ai|α near u = ai, 0 < α < 2. Such solutions are, over large regions, identically equal to some zeroes of the potential ai’s. We establish the estimates Ln(I0 ∩ Br (x0)) ≤ c1r n−1 , Hn−1(∂∗I0 ∩ Br (x0)) ≥ c2r n−1 , r ≥ r0(x0) for the diffuse interface I0 := {x ∈ Rn : min1≤i≤N |u(x)− ai | > 0} and the free boundary ∂I0. Furthermore, if α = 1 we establish the upper bound Hn−1(∂∗I0 ∩ Br (x0)) ≤ c3r n−1 , r ≥ r0(x0).
publishDate 2021
dc.date.none.fl_str_mv 2021
2025
2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/1996
url http://hdl.handle.net/20.500.11824/1996
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:BIRD. BCAM's Institutional Repository Data
instname:Basque Center for Applied Mathematics (BCAM)
instname_str Basque Center for Applied Mathematics (BCAM)
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collection BIRD. BCAM's Institutional Repository Data
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