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dc.contributor.author
Lederman, Claudia Beatriz
dc.contributor.author
Wolanski, Noemi Irene
dc.date.available
2024-09-20T10:57:57Z
dc.date.issued
2008-12
dc.identifier.citation
Lederman, Claudia Beatriz; Wolanski, Noemi Irene; A local monotonicity formula for an inhomogenous singular perturbation problem and applications; Springer Heidelberg; Annali Di Matematica Pura Ed Applicata; 187; 2; 12-2008; 197-220
dc.identifier.issn
0373-3114
dc.identifier.uri
http://hdl.handle.net/11336/244687
dc.description.abstract
In this paper we prove a local monotonicity formula for solutions to an inhomogeneous singularly perturbed diffusion problem of interest in combustion. This type of monotonicity formula has proved to be very useful for the study of the regularity of limits u of solutions of the singular perturbation problem and of ∂{u > 0}, in the global homogeneous case. As a consequence of this formula we prove that u has an asymptotic development at every point in ∂{u > 0} where there is a nonhorizontal tangent ball. These kind of developments have been essential for the proof of the regularity of ∂{u > 0} for Bernoulli and Stefan free boundary problems. We also present applications of our results to the study of the regularity of ∂{u > 0} in the stationary case including, in particular, its regularity in the case of energy minimizers. We present as well a regularity result for traveling waves of a combustion model that relies on our monotonicity formula and its consequences.The fact that our results hold for the inhomogeneous problem allows a very wide applicability. Indeed, they may be applied to problems with nonlocal diffusion and/or transport.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer Heidelberg
dc.rights
info:eu-repo/semantics/restrictedAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
SINGULAR PERTURBATION PROBLEMS
dc.subject
MONOTONICITY FORMULA
dc.subject
INHOMOGENEOUS PROBLEMS
dc.subject
COMBUSTION
dc.subject.classification
Matemática Aplicada
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
A local monotonicity formula for an inhomogenous singular perturbation problem and applications
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2024-09-03T13:17:55Z
dc.journal.volume
187
dc.journal.number
2
dc.journal.pagination
197-220
dc.journal.pais
Alemania
dc.journal.ciudad
Heidelberg
dc.description.fil
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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
dc.description.fil
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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
dc.journal.title
Annali Di Matematica Pura Ed Applicata
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s10231-007-0041-6
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s10231-007-0041-6
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