A local monotonicity formula for an inhomogeneous singular perturbation problem and applications: Part II

Autores
Lederman, Claudia Beatriz; Wolanski, Noemi Irene
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we continue with our work in Lederman and Wolanski (Ann Math Pura Appl 187(2):197–220, 2008) where we developed a local monotonicity formula for solutions to an inhomogeneous singular perturbation problem of interest in combustion theory. There we proved local monotonicity formulae for solutions uε to the singular perturbation problem and for u = lim uε, assuming that both uε and u were defined in an arbitrary domain D in RN+1. In the present work we obtain global monotonicity formulae for limit functions u that are globally defined, while uε are not. We derive such global formulae from a local one that we prove here. In particular, we obtain a global monotonicity formula for blow up limits u0 of limit functions u that are not globally defined. As a consequence of this formula, we characterize blow up limits u0 in terms of the value of a density at the blow up point. We also present applications of the results in this paper to the study of the regularity of ∂{u > 0} (the flame front in combustion models). The fact that our results hold for the inhomogeneous singular perturbation problem allows a very wide applicability, for instance to problems with nonlocal diffusion and/or transport.
Fil: Lederman, Claudia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Wolanski, Noemi Irene. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
SINGULAR PERTURBATION PROBLEM
MONOTONICITY FORMULA
INHOMOGENEOUS PROBLEM
COMBUSTION
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/245236
Acceder
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network_name_str CONICET Digital (CONICET)
spelling A local monotonicity formula for an inhomogeneous singular perturbation problem and applications: Part IILederman, Claudia BeatrizWolanski, Noemi IreneSINGULAR PERTURBATION PROBLEMMONOTONICITY FORMULAINHOMOGENEOUS PROBLEMCOMBUSTIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we continue with our work in Lederman and Wolanski (Ann Math Pura Appl 187(2):197–220, 2008) where we developed a local monotonicity formula for solutions to an inhomogeneous singular perturbation problem of interest in combustion theory. There we proved local monotonicity formulae for solutions uε to the singular perturbation problem and for u = lim uε, assuming that both uε and u were defined in an arbitrary domain D in RN+1. In the present work we obtain global monotonicity formulae for limit functions u that are globally defined, while uε are not. We derive such global formulae from a local one that we prove here. In particular, we obtain a global monotonicity formula for blow up limits u0 of limit functions u that are not globally defined. As a consequence of this formula, we characterize blow up limits u0 in terms of the value of a density at the blow up point. We also present applications of the results in this paper to the study of the regularity of ∂{u > 0} (the flame front in combustion models). The fact that our results hold for the inhomogeneous singular perturbation problem allows a very wide applicability, for instance to problems with nonlocal diffusion and/or transport.Fil: Lederman, Claudia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Wolanski, Noemi Irene. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaSpringer Heidelberg2010-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/245236Lederman, Claudia Beatriz; Wolanski, Noemi Irene; A local monotonicity formula for an inhomogeneous singular perturbation problem and applications: Part II; Springer Heidelberg; Annali Di Matematica Pura Ed Applicata; 189; 1; 6-2010; 25-460373-3114CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s10231-009-0099-4info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s10231-009-0099-4info:eu-repo/semantics/altIdentifier/url/https://mate.dm.uba.ar/~wolanski/papers/monoII.pdfinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:03:59Zoai:ri.conicet.gov.ar:11336/245236instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:03:59.916CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A local monotonicity formula for an inhomogeneous singular perturbation problem and applications: Part II
title A local monotonicity formula for an inhomogeneous singular perturbation problem and applications: Part II
spellingShingle A local monotonicity formula for an inhomogeneous singular perturbation problem and applications: Part II
Lederman, Claudia Beatriz
SINGULAR PERTURBATION PROBLEM
MONOTONICITY FORMULA
INHOMOGENEOUS PROBLEM
COMBUSTION
title_short A local monotonicity formula for an inhomogeneous singular perturbation problem and applications: Part II
title_full A local monotonicity formula for an inhomogeneous singular perturbation problem and applications: Part II
title_fullStr A local monotonicity formula for an inhomogeneous singular perturbation problem and applications: Part II
title_full_unstemmed A local monotonicity formula for an inhomogeneous singular perturbation problem and applications: Part II
title_sort A local monotonicity formula for an inhomogeneous singular perturbation problem and applications: Part II
dc.creator.none.fl_str_mv Lederman, Claudia Beatriz
Wolanski, Noemi Irene
author Lederman, Claudia Beatriz
author_facet Lederman, Claudia Beatriz
Wolanski, Noemi Irene
author_role author
author2 Wolanski, Noemi Irene
author2_role author
dc.subject.none.fl_str_mv SINGULAR PERTURBATION PROBLEM
MONOTONICITY FORMULA
INHOMOGENEOUS PROBLEM
COMBUSTION
topic SINGULAR PERTURBATION PROBLEM
MONOTONICITY FORMULA
INHOMOGENEOUS PROBLEM
COMBUSTION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper we continue with our work in Lederman and Wolanski (Ann Math Pura Appl 187(2):197–220, 2008) where we developed a local monotonicity formula for solutions to an inhomogeneous singular perturbation problem of interest in combustion theory. There we proved local monotonicity formulae for solutions uε to the singular perturbation problem and for u = lim uε, assuming that both uε and u were defined in an arbitrary domain D in RN+1. In the present work we obtain global monotonicity formulae for limit functions u that are globally defined, while uε are not. We derive such global formulae from a local one that we prove here. In particular, we obtain a global monotonicity formula for blow up limits u0 of limit functions u that are not globally defined. As a consequence of this formula, we characterize blow up limits u0 in terms of the value of a density at the blow up point. We also present applications of the results in this paper to the study of the regularity of ∂{u > 0} (the flame front in combustion models). The fact that our results hold for the inhomogeneous singular perturbation problem allows a very wide applicability, for instance to problems with nonlocal diffusion and/or transport.
Fil: Lederman, Claudia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Wolanski, Noemi Irene. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description In this paper we continue with our work in Lederman and Wolanski (Ann Math Pura Appl 187(2):197–220, 2008) where we developed a local monotonicity formula for solutions to an inhomogeneous singular perturbation problem of interest in combustion theory. There we proved local monotonicity formulae for solutions uε to the singular perturbation problem and for u = lim uε, assuming that both uε and u were defined in an arbitrary domain D in RN+1. In the present work we obtain global monotonicity formulae for limit functions u that are globally defined, while uε are not. We derive such global formulae from a local one that we prove here. In particular, we obtain a global monotonicity formula for blow up limits u0 of limit functions u that are not globally defined. As a consequence of this formula, we characterize blow up limits u0 in terms of the value of a density at the blow up point. We also present applications of the results in this paper to the study of the regularity of ∂{u > 0} (the flame front in combustion models). The fact that our results hold for the inhomogeneous singular perturbation problem allows a very wide applicability, for instance to problems with nonlocal diffusion and/or transport.
publishDate 2010
dc.date.none.fl_str_mv 2010-06
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/245236
Lederman, Claudia Beatriz; Wolanski, Noemi Irene; A local monotonicity formula for an inhomogeneous singular perturbation problem and applications: Part II; Springer Heidelberg; Annali Di Matematica Pura Ed Applicata; 189; 1; 6-2010; 25-46
0373-3114
CONICET Digital
CONICET
url http://hdl.handle.net/11336/245236
identifier_str_mv Lederman, Claudia Beatriz; Wolanski, Noemi Irene; A local monotonicity formula for an inhomogeneous singular perturbation problem and applications: Part II; Springer Heidelberg; Annali Di Matematica Pura Ed Applicata; 189; 1; 6-2010; 25-46
0373-3114
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s10231-009-0099-4
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s10231-009-0099-4
info:eu-repo/semantics/altIdentifier/url/https://mate.dm.uba.ar/~wolanski/papers/monoII.pdf
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer Heidelberg
publisher.none.fl_str_mv Springer Heidelberg
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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