Regularity for degenerate evolution equations with strong absorption

Autores
Da Silva, Joao Vitor; Ochoa, Pablo Daniel; Silva, Analia
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this manuscript, we study geometric regularity estimates for degenerate parabolic equations of p-Laplacian type (2 ≤ p < ∞) under a strong absorption condition: Δpu − ∂u/∂t = λ0uq + in ΩT := Ω × (0,T), where 0 ≤ q < 1. This model is interesting because it yields the formation of dead-core sets, i.e., regions where non-negative solutions vanish identically. We shall prove sharp and improved parabolic Cα regularity estimates along the set F0(u, ΩT) = ∂{u > 0} ∩ΩT (the free boundary), where α = p/p−1−q ≥ 1 + 1/p−1. Some weak geometric and measure theoretical properties as non-degeneracy, positive density, porosity and finite speed of propagation are proved. As an application, we prove a Liouville-type result for entire solutions. A specific analysis for Blow-up type solutions will be done as well. The results are new even for dead-core problems driven by the heat operator.
Fil: Da Silva, Joao Vitor. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Ochoa, Pablo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Cuyo; Argentina
Fil: Silva, Analia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina
Materia
DEAD-CORE PROBLEMS
LIOUVILLE TYPE RESULTS
P-LAPLACIAN TYPE OPERATORS
SHARP AND IMPROVED INTRINSIC REGULARITY
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:11336/92427
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/92427
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Regularity for degenerate evolution equations with strong absorptionDa Silva, Joao VitorOchoa, Pablo DanielSilva, AnaliaDEAD-CORE PROBLEMSLIOUVILLE TYPE RESULTSP-LAPLACIAN TYPE OPERATORSSHARP AND IMPROVED INTRINSIC REGULARITYhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this manuscript, we study geometric regularity estimates for degenerate parabolic equations of p-Laplacian type (2 ≤ p < ∞) under a strong absorption condition: Δpu − ∂u/∂t = λ0uq + in ΩT := Ω × (0,T), where 0 ≤ q < 1. This model is interesting because it yields the formation of dead-core sets, i.e., regions where non-negative solutions vanish identically. We shall prove sharp and improved parabolic Cα regularity estimates along the set F0(u, ΩT) = ∂{u > 0} ∩ΩT (the free boundary), where α = p/p−1−q ≥ 1 + 1/p−1. Some weak geometric and measure theoretical properties as non-degeneracy, positive density, porosity and finite speed of propagation are proved. As an application, we prove a Liouville-type result for entire solutions. A specific analysis for Blow-up type solutions will be done as well. The results are new even for dead-core problems driven by the heat operator.Fil: Da Silva, Joao Vitor. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Ochoa, Pablo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Cuyo; ArgentinaFil: Silva, Analia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; ArgentinaAcademic Press Inc Elsevier Science2018-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/92427Da Silva, Joao Vitor; Ochoa, Pablo Daniel; Silva, Analia; Regularity for degenerate evolution equations with strong absorption; Academic Press Inc Elsevier Science; Journal Of Differential Equations; 264; 12; 6-2018; 7270-72930022-0396CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://linkinghub.elsevier.com/retrieve/pii/S0022039618300962info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jde.2018.02.013info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:09:14Zoai:ri.conicet.gov.ar:11336/92427instacron: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 12:09:14.965CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Regularity for degenerate evolution equations with strong absorption
title Regularity for degenerate evolution equations with strong absorption
spellingShingle Regularity for degenerate evolution equations with strong absorption
Da Silva, Joao Vitor
DEAD-CORE PROBLEMS
LIOUVILLE TYPE RESULTS
P-LAPLACIAN TYPE OPERATORS
SHARP AND IMPROVED INTRINSIC REGULARITY
title_short Regularity for degenerate evolution equations with strong absorption
title_full Regularity for degenerate evolution equations with strong absorption
title_fullStr Regularity for degenerate evolution equations with strong absorption
title_full_unstemmed Regularity for degenerate evolution equations with strong absorption
title_sort Regularity for degenerate evolution equations with strong absorption
dc.creator.none.fl_str_mv Da Silva, Joao Vitor
Ochoa, Pablo Daniel
Silva, Analia
author Da Silva, Joao Vitor
author_facet Da Silva, Joao Vitor
Ochoa, Pablo Daniel
Silva, Analia
author_role author
author2 Ochoa, Pablo Daniel
Silva, Analia
author2_role author
author
dc.subject.none.fl_str_mv DEAD-CORE PROBLEMS
LIOUVILLE TYPE RESULTS
P-LAPLACIAN TYPE OPERATORS
SHARP AND IMPROVED INTRINSIC REGULARITY
topic DEAD-CORE PROBLEMS
LIOUVILLE TYPE RESULTS
P-LAPLACIAN TYPE OPERATORS
SHARP AND IMPROVED INTRINSIC REGULARITY
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this manuscript, we study geometric regularity estimates for degenerate parabolic equations of p-Laplacian type (2 ≤ p < ∞) under a strong absorption condition: Δpu − ∂u/∂t = λ0uq + in ΩT := Ω × (0,T), where 0 ≤ q < 1. This model is interesting because it yields the formation of dead-core sets, i.e., regions where non-negative solutions vanish identically. We shall prove sharp and improved parabolic Cα regularity estimates along the set F0(u, ΩT) = ∂{u > 0} ∩ΩT (the free boundary), where α = p/p−1−q ≥ 1 + 1/p−1. Some weak geometric and measure theoretical properties as non-degeneracy, positive density, porosity and finite speed of propagation are proved. As an application, we prove a Liouville-type result for entire solutions. A specific analysis for Blow-up type solutions will be done as well. The results are new even for dead-core problems driven by the heat operator.
Fil: Da Silva, Joao Vitor. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Ochoa, Pablo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Cuyo; Argentina
Fil: Silva, Analia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina
description In this manuscript, we study geometric regularity estimates for degenerate parabolic equations of p-Laplacian type (2 ≤ p < ∞) under a strong absorption condition: Δpu − ∂u/∂t = λ0uq + in ΩT := Ω × (0,T), where 0 ≤ q < 1. This model is interesting because it yields the formation of dead-core sets, i.e., regions where non-negative solutions vanish identically. We shall prove sharp and improved parabolic Cα regularity estimates along the set F0(u, ΩT) = ∂{u > 0} ∩ΩT (the free boundary), where α = p/p−1−q ≥ 1 + 1/p−1. Some weak geometric and measure theoretical properties as non-degeneracy, positive density, porosity and finite speed of propagation are proved. As an application, we prove a Liouville-type result for entire solutions. A specific analysis for Blow-up type solutions will be done as well. The results are new even for dead-core problems driven by the heat operator.
publishDate 2018
dc.date.none.fl_str_mv 2018-06
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/11336/92427
Da Silva, Joao Vitor; Ochoa, Pablo Daniel; Silva, Analia; Regularity for degenerate evolution equations with strong absorption; Academic Press Inc Elsevier Science; Journal Of Differential Equations; 264; 12; 6-2018; 7270-7293
0022-0396
CONICET Digital
CONICET
url http://hdl.handle.net/11336/92427
identifier_str_mv Da Silva, Joao Vitor; Ochoa, Pablo Daniel; Silva, Analia; Regularity for degenerate evolution equations with strong absorption; Academic Press Inc Elsevier Science; Journal Of Differential Equations; 264; 12; 6-2018; 7270-7293
0022-0396
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://linkinghub.elsevier.com/retrieve/pii/S0022039618300962
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jde.2018.02.013
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
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
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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