Parabolic mean values and maximal estimates for gradients of temperatures
- Autores
- Aimar, Hugo Alejandro; Gomez, Ivana Daniela; Iaffei, Bibiana Raquel
- Año de publicación
- 2008
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- We aim to prove inequalities of the form | δk - λ (x, t) ∇k u (x, t) | ≤ C MR+- MD#, λ, k u (x, t) for solutions of frac(∂ u, ∂ t) = Δ u on a domain Ω = D × R+, where δ (x, t) is the parabolic distance of (x, t) to parabolic boundary of Ω, MR+- is the one-sided Hardy-Littlewood maximal operator in the time variable on R+, MD#, λ, k is a Calderón-Scott type d-dimensional elliptic maximal operator in the space variable on the domain D in Rd, and 0 < λ < k < λ + d. As a consequence, when D is a bounded Lipschitz domain, we obtain estimates for the Lp (Ω) norm of δ2 n - λ (∇2, 1)n u in terms of some mixed norm ∫0∞ {norm of matrix} u (ṡ, t) {norm of matrix}Bpλ, p (D)p d t for the space Lp (R+, Bpλ, p (D)) with {norm of matrix} ṡ {norm of matrix}Bpλ, p (D) denotes the Besov norm in the space variable x and where ∇2, 1 = (∇2, frac(∂, ∂ t)).
Fil: Aimar, Hugo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Gomez, Ivana Daniela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Iaffei, Bibiana Raquel. Universidad Nacional del Litoral; Argentina - Materia
-
GRADIENT ESTIMATES
HEAT EQUATION
MAXIMAL OPERATORS
MEAN VALUE FORMULA - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/84272
Ver los metadatos del registro completo
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Parabolic mean values and maximal estimates for gradients of temperaturesAimar, Hugo AlejandroGomez, Ivana DanielaIaffei, Bibiana RaquelGRADIENT ESTIMATESHEAT EQUATIONMAXIMAL OPERATORSMEAN VALUE FORMULAhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We aim to prove inequalities of the form | δk - λ (x, t) ∇k u (x, t) | ≤ C MR+- MD#, λ, k u (x, t) for solutions of frac(∂ u, ∂ t) = Δ u on a domain Ω = D × R+, where δ (x, t) is the parabolic distance of (x, t) to parabolic boundary of Ω, MR+- is the one-sided Hardy-Littlewood maximal operator in the time variable on R+, MD#, λ, k is a Calderón-Scott type d-dimensional elliptic maximal operator in the space variable on the domain D in Rd, and 0 < λ < k < λ + d. As a consequence, when D is a bounded Lipschitz domain, we obtain estimates for the Lp (Ω) norm of δ2 n - λ (∇2, 1)n u in terms of some mixed norm ∫0∞ {norm of matrix} u (ṡ, t) {norm of matrix}Bpλ, p (D)p d t for the space Lp (R+, Bpλ, p (D)) with {norm of matrix} ṡ {norm of matrix}Bpλ, p (D) denotes the Besov norm in the space variable x and where ∇2, 1 = (∇2, frac(∂, ∂ t)).Fil: Aimar, Hugo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Gomez, Ivana Daniela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Iaffei, Bibiana Raquel. Universidad Nacional del Litoral; ArgentinaAcademic Press Inc Elsevier Science2008-10info: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/11336/84272Aimar, Hugo Alejandro; Gomez, Ivana Daniela; Iaffei, Bibiana Raquel; Parabolic mean values and maximal estimates for gradients of temperatures; Academic Press Inc Elsevier Science; Journal of Functional Analysis; 255; 8; 10-2008; 1939-19560022-1236CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jfa.2008.06.006info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:30:00Zoai:ri.conicet.gov.ar:11336/84272instacron: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:34982025-09-29 10:30:00.331CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
| dc.title.none.fl_str_mv |
Parabolic mean values and maximal estimates for gradients of temperatures |
| title |
Parabolic mean values and maximal estimates for gradients of temperatures |
| spellingShingle |
Parabolic mean values and maximal estimates for gradients of temperatures Aimar, Hugo Alejandro GRADIENT ESTIMATES HEAT EQUATION MAXIMAL OPERATORS MEAN VALUE FORMULA |
| title_short |
Parabolic mean values and maximal estimates for gradients of temperatures |
| title_full |
Parabolic mean values and maximal estimates for gradients of temperatures |
| title_fullStr |
Parabolic mean values and maximal estimates for gradients of temperatures |
| title_full_unstemmed |
Parabolic mean values and maximal estimates for gradients of temperatures |
| title_sort |
Parabolic mean values and maximal estimates for gradients of temperatures |
| dc.creator.none.fl_str_mv |
Aimar, Hugo Alejandro Gomez, Ivana Daniela Iaffei, Bibiana Raquel |
| author |
Aimar, Hugo Alejandro |
| author_facet |
Aimar, Hugo Alejandro Gomez, Ivana Daniela Iaffei, Bibiana Raquel |
| author_role |
author |
| author2 |
Gomez, Ivana Daniela Iaffei, Bibiana Raquel |
| author2_role |
author author |
| dc.subject.none.fl_str_mv |
GRADIENT ESTIMATES HEAT EQUATION MAXIMAL OPERATORS MEAN VALUE FORMULA |
| topic |
GRADIENT ESTIMATES HEAT EQUATION MAXIMAL OPERATORS MEAN VALUE FORMULA |
| purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| dc.description.none.fl_txt_mv |
We aim to prove inequalities of the form | δk - λ (x, t) ∇k u (x, t) | ≤ C MR+- MD#, λ, k u (x, t) for solutions of frac(∂ u, ∂ t) = Δ u on a domain Ω = D × R+, where δ (x, t) is the parabolic distance of (x, t) to parabolic boundary of Ω, MR+- is the one-sided Hardy-Littlewood maximal operator in the time variable on R+, MD#, λ, k is a Calderón-Scott type d-dimensional elliptic maximal operator in the space variable on the domain D in Rd, and 0 < λ < k < λ + d. As a consequence, when D is a bounded Lipschitz domain, we obtain estimates for the Lp (Ω) norm of δ2 n - λ (∇2, 1)n u in terms of some mixed norm ∫0∞ {norm of matrix} u (ṡ, t) {norm of matrix}Bpλ, p (D)p d t for the space Lp (R+, Bpλ, p (D)) with {norm of matrix} ṡ {norm of matrix}Bpλ, p (D) denotes the Besov norm in the space variable x and where ∇2, 1 = (∇2, frac(∂, ∂ t)). Fil: Aimar, Hugo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina Fil: Gomez, Ivana Daniela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina Fil: Iaffei, Bibiana Raquel. Universidad Nacional del Litoral; Argentina |
| description |
We aim to prove inequalities of the form | δk - λ (x, t) ∇k u (x, t) | ≤ C MR+- MD#, λ, k u (x, t) for solutions of frac(∂ u, ∂ t) = Δ u on a domain Ω = D × R+, where δ (x, t) is the parabolic distance of (x, t) to parabolic boundary of Ω, MR+- is the one-sided Hardy-Littlewood maximal operator in the time variable on R+, MD#, λ, k is a Calderón-Scott type d-dimensional elliptic maximal operator in the space variable on the domain D in Rd, and 0 < λ < k < λ + d. As a consequence, when D is a bounded Lipschitz domain, we obtain estimates for the Lp (Ω) norm of δ2 n - λ (∇2, 1)n u in terms of some mixed norm ∫0∞ {norm of matrix} u (ṡ, t) {norm of matrix}Bpλ, p (D)p d t for the space Lp (R+, Bpλ, p (D)) with {norm of matrix} ṡ {norm of matrix}Bpλ, p (D) denotes the Besov norm in the space variable x and where ∇2, 1 = (∇2, frac(∂, ∂ t)). |
| publishDate |
2008 |
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2008-10 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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article |
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publishedVersion |
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http://hdl.handle.net/11336/84272 Aimar, Hugo Alejandro; Gomez, Ivana Daniela; Iaffei, Bibiana Raquel; Parabolic mean values and maximal estimates for gradients of temperatures; Academic Press Inc Elsevier Science; Journal of Functional Analysis; 255; 8; 10-2008; 1939-1956 0022-1236 CONICET Digital CONICET |
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http://hdl.handle.net/11336/84272 |
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Aimar, Hugo Alejandro; Gomez, Ivana Daniela; Iaffei, Bibiana Raquel; Parabolic mean values and maximal estimates for gradients of temperatures; Academic Press Inc Elsevier Science; Journal of Functional Analysis; 255; 8; 10-2008; 1939-1956 0022-1236 CONICET Digital CONICET |
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eng |
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eng |
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Academic Press Inc Elsevier Science |
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Academic Press Inc Elsevier Science |
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