Traces for fractional Sobolev spaces with variable exponents

Autores
del Pezzo, Leandro Martin; Rossi, Julio Daniel
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this note we prove a trace theorem in fractional spaces with variable exponents. To be more precise, we show that if p: Ω × Ω → (1,∞) and q : ∂Ω → (1,∞) are continuous functions such that (n − 1)p(x, x) n − sp(x, x) > q(x) in ∂Ω ∩ {x ∈ Ω: n − sp(x, x) > 0}, then the inequality kfkL q(·) (∂Ω) ≤ C n kfkL p¯(·) (Ω) + [f]s,p(·,·) o holds. Here ¯p(x) = p(x, x) and [f]s,p(·,·) denotes the fractional seminorm with variable exponent, that is given by [f]s,p(·,·) := inf λ > 0: Z Ω Z Ω |f(x) − f(y)| p(x,y) λp(x,y) |x − y| n+sp(x,y) dxdy < 1 and kfkL q(·) (∂Ω) and kfkL p¯(·) (Ω) are the usual Lebesgue norms with variable exponent.
Fil: del Pezzo, Leandro Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella; Argentina
Fil: Rossi, Julio Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Materia
TRACES
FRACTIONAL
SOBOLEV
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:11336/75218
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/75218
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Traces for fractional Sobolev spaces with variable exponentsdel Pezzo, Leandro MartinRossi, Julio DanielTRACESFRACTIONALSOBOLEVhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this note we prove a trace theorem in fractional spaces with variable exponents. To be more precise, we show that if p: Ω × Ω → (1,∞) and q : ∂Ω → (1,∞) are continuous functions such that (n − 1)p(x, x) n − sp(x, x) > q(x) in ∂Ω ∩ {x ∈ Ω: n − sp(x, x) > 0}, then the inequality kfkL q(·) (∂Ω) ≤ C n kfkL p¯(·) (Ω) + [f]s,p(·,·) o holds. Here ¯p(x) = p(x, x) and [f]s,p(·,·) denotes the fractional seminorm with variable exponent, that is given by [f]s,p(·,·) := inf λ > 0: Z Ω Z Ω |f(x) − f(y)| p(x,y) λp(x,y) |x − y| n+sp(x,y) dxdy < 1 and kfkL q(·) (∂Ω) and kfkL p¯(·) (Ω) are the usual Lebesgue norms with variable exponent.Fil: del Pezzo, Leandro Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella; ArgentinaFil: Rossi, Julio Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaTusi Mathematical Research Group2017-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/75218del Pezzo, Leandro Martin; Rossi, Julio Daniel; Traces for fractional Sobolev spaces with variable exponents; Tusi Mathematical Research Group; Advances in Operator Theory; 2; 4; 9-2017; 435-4462538-225XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/ 10.22034/aot.1704-1152info:eu-repo/semantics/altIdentifier/url/https://projecteuclid.org/euclid.aot/1512431720info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:07:56Zoai:ri.conicet.gov.ar:11336/75218instacron: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:34982025-09-03 10:07:56.701CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Traces for fractional Sobolev spaces with variable exponents
title Traces for fractional Sobolev spaces with variable exponents
spellingShingle Traces for fractional Sobolev spaces with variable exponents
del Pezzo, Leandro Martin
TRACES
FRACTIONAL
SOBOLEV
title_short Traces for fractional Sobolev spaces with variable exponents
title_full Traces for fractional Sobolev spaces with variable exponents
title_fullStr Traces for fractional Sobolev spaces with variable exponents
title_full_unstemmed Traces for fractional Sobolev spaces with variable exponents
title_sort Traces for fractional Sobolev spaces with variable exponents
dc.creator.none.fl_str_mv del Pezzo, Leandro Martin
Rossi, Julio Daniel
author del Pezzo, Leandro Martin
author_facet del Pezzo, Leandro Martin
Rossi, Julio Daniel
author_role author
author2 Rossi, Julio Daniel
author2_role author
dc.subject.none.fl_str_mv TRACES
FRACTIONAL
SOBOLEV
topic TRACES
FRACTIONAL
SOBOLEV
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 note we prove a trace theorem in fractional spaces with variable exponents. To be more precise, we show that if p: Ω × Ω → (1,∞) and q : ∂Ω → (1,∞) are continuous functions such that (n − 1)p(x, x) n − sp(x, x) > q(x) in ∂Ω ∩ {x ∈ Ω: n − sp(x, x) > 0}, then the inequality kfkL q(·) (∂Ω) ≤ C n kfkL p¯(·) (Ω) + [f]s,p(·,·) o holds. Here ¯p(x) = p(x, x) and [f]s,p(·,·) denotes the fractional seminorm with variable exponent, that is given by [f]s,p(·,·) := inf λ > 0: Z Ω Z Ω |f(x) − f(y)| p(x,y) λp(x,y) |x − y| n+sp(x,y) dxdy < 1 and kfkL q(·) (∂Ω) and kfkL p¯(·) (Ω) are the usual Lebesgue norms with variable exponent.
Fil: del Pezzo, Leandro Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella; Argentina
Fil: Rossi, Julio Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
description In this note we prove a trace theorem in fractional spaces with variable exponents. To be more precise, we show that if p: Ω × Ω → (1,∞) and q : ∂Ω → (1,∞) are continuous functions such that (n − 1)p(x, x) n − sp(x, x) > q(x) in ∂Ω ∩ {x ∈ Ω: n − sp(x, x) > 0}, then the inequality kfkL q(·) (∂Ω) ≤ C n kfkL p¯(·) (Ω) + [f]s,p(·,·) o holds. Here ¯p(x) = p(x, x) and [f]s,p(·,·) denotes the fractional seminorm with variable exponent, that is given by [f]s,p(·,·) := inf λ > 0: Z Ω Z Ω |f(x) − f(y)| p(x,y) λp(x,y) |x − y| n+sp(x,y) dxdy < 1 and kfkL q(·) (∂Ω) and kfkL p¯(·) (Ω) are the usual Lebesgue norms with variable exponent.
publishDate 2017
dc.date.none.fl_str_mv 2017-09
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/11336/75218
del Pezzo, Leandro Martin; Rossi, Julio Daniel; Traces for fractional Sobolev spaces with variable exponents; Tusi Mathematical Research Group; Advances in Operator Theory; 2; 4; 9-2017; 435-446
2538-225X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/75218
identifier_str_mv del Pezzo, Leandro Martin; Rossi, Julio Daniel; Traces for fractional Sobolev spaces with variable exponents; Tusi Mathematical Research Group; Advances in Operator Theory; 2; 4; 9-2017; 435-446
2538-225X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/ 10.22034/aot.1704-1152
info:eu-repo/semantics/altIdentifier/url/https://projecteuclid.org/euclid.aot/1512431720
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 Tusi Mathematical Research Group
publisher.none.fl_str_mv Tusi Mathematical Research Group
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 13.13397

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