Pointwise monotonicity of heat kernels

In this paper we present an elementary proof of a pointwise radial monotonicity property of heat kernels that is shared by the Euclidean spaces, spheres and hyperbolic spaces. The main result was discovered by Cheeger and Yau in 1981 and rediscovered in special cases during the last few years. It de...

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Detalles Bibliográficos
Autores: Alonso-Orán, Diego, Chamizo Lorente, Fernando, Martínez, Ángel D., Mas, Albert
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/706651
Acceso en línea:http://hdl.handle.net/10486/706651
https://dx.doi.org/10.1007/s13163-021-00417-8
Access Level:acceso abierto
Palabra clave:Fractional Laplacian
Heat Kernel
Pointwise Inequalities
Maximum Principle
Matemáticas
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spelling Pointwise monotonicity of heat kernelsAlonso-Orán, DiegoChamizo Lorente, FernandoMartínez, Ángel D.Mas, AlbertFractional LaplacianHeat KernelPointwise InequalitiesMaximum PrincipleMatemáticasIn this paper we present an elementary proof of a pointwise radial monotonicity property of heat kernels that is shared by the Euclidean spaces, spheres and hyperbolic spaces. The main result was discovered by Cheeger and Yau in 1981 and rediscovered in special cases during the last few years. It deals with the monotonicity of the heat kernel from special points on revolution hypersurfaces. Our proof hinges on a non straightforward but elementary application of the parabolic maximum principle. As a consequence of the monotonicity property, we derive new inequalities involving classical special functionsSpringerDepartamento de MatemáticasFacultad de Ciencias20212021-12-13research articlehttp://purl.org/coar/resource_type/c_2df8fbb1VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10486/706651https://dx.doi.org/10.1007/s13163-021-00417-8reponame:Biblos-e Archivo. Repositorio Institucional de la UAMinstname:Universidad Autónoma de MadridInglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:repositorio.uam.es:10486/7066512026-06-23T12:46:27Z
dc.title.none.fl_str_mv Pointwise monotonicity of heat kernels
title Pointwise monotonicity of heat kernels
spellingShingle Pointwise monotonicity of heat kernels
Alonso-Orán, Diego
Fractional Laplacian
Heat Kernel
Pointwise Inequalities
Maximum Principle
Matemáticas
title_short Pointwise monotonicity of heat kernels
title_full Pointwise monotonicity of heat kernels
title_fullStr Pointwise monotonicity of heat kernels
title_full_unstemmed Pointwise monotonicity of heat kernels
title_sort Pointwise monotonicity of heat kernels
dc.creator.none.fl_str_mv Alonso-Orán, Diego
Chamizo Lorente, Fernando
Martínez, Ángel D.
Mas, Albert
author Alonso-Orán, Diego
author_facet Alonso-Orán, Diego
Chamizo Lorente, Fernando
Martínez, Ángel D.
Mas, Albert
author_role author
author2 Chamizo Lorente, Fernando
Martínez, Ángel D.
Mas, Albert
author2_role author
author
author
dc.contributor.none.fl_str_mv Departamento de Matemáticas
Facultad de Ciencias
dc.subject.none.fl_str_mv Fractional Laplacian
Heat Kernel
Pointwise Inequalities
Maximum Principle
Matemáticas
topic Fractional Laplacian
Heat Kernel
Pointwise Inequalities
Maximum Principle
Matemáticas
description In this paper we present an elementary proof of a pointwise radial monotonicity property of heat kernels that is shared by the Euclidean spaces, spheres and hyperbolic spaces. The main result was discovered by Cheeger and Yau in 1981 and rediscovered in special cases during the last few years. It deals with the monotonicity of the heat kernel from special points on revolution hypersurfaces. Our proof hinges on a non straightforward but elementary application of the parabolic maximum principle. As a consequence of the monotonicity property, we derive new inequalities involving classical special functions
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-12-13
dc.type.none.fl_str_mv research article
http://purl.org/coar/resource_type/c_2df8fbb1
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10486/706651
https://dx.doi.org/10.1007/s13163-021-00417-8
url http://hdl.handle.net/10486/706651
https://dx.doi.org/10.1007/s13163-021-00417-8
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Biblos-e Archivo. Repositorio Institucional de la UAM
instname:Universidad Autónoma de Madrid
instname_str Universidad Autónoma de Madrid
reponame_str Biblos-e Archivo. Repositorio Institucional de la UAM
collection Biblos-e Archivo. Repositorio Institucional de la UAM
repository.name.fl_str_mv
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