Uniformly elliptic equations with concave growth in the gradient and measures
- Autores
- de Borbón, María Laura; Ochoa, Pablo Daniel
- Año de publicación
- 2024
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- We deal with quasilinear elliptic problems with measure data:Lw = H(x, w, ∇w) + µ in Ωw = 0 on ∂Ω,(0.1)where Lw := −div(A(x)∇w) with A = A(x) a bounded, coercive, and symmetric matrix field, theHamiltonian H has at most q-growth in the gradient for 0 < q < 1, and µ is any Radon measure.We employ the compactness of the Green operator associated to L from the space of measures toW1,p0(Ω) for all p ∈ [1, N/(N − 1)) together with fixed point arguments to solve problem (0.1) forany measure µ. Moreover, we provide explicit estimates of the solution in terms of the data. As anapplication, stability results are given. We also give conditions for the existence of W1,20-solutionsthrough the classic theory of monotone and coercive operators. In any case, we do not impose anysize restriction on µ and any sign condition on H.
Fil: de Borbón, María Laura. Universidad Nacional de Cuyo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina
Fil: Ochoa, Pablo Daniel. Universidad Nacional de Cuyo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina - Materia
-
Quasilinear elliptic equations
Fixed point
Green’s functions
Weak solutions
Uniqueness - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/231140
Ver los metadatos del registro completo
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Uniformly elliptic equations with concave growth in the gradient and measuresde Borbón, María LauraOchoa, Pablo DanielQuasilinear elliptic equationsFixed pointGreen’s functionsWeak solutionsUniquenesshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We deal with quasilinear elliptic problems with measure data:Lw = H(x, w, ∇w) + µ in Ωw = 0 on ∂Ω,(0.1)where Lw := −div(A(x)∇w) with A = A(x) a bounded, coercive, and symmetric matrix field, theHamiltonian H has at most q-growth in the gradient for 0 < q < 1, and µ is any Radon measure.We employ the compactness of the Green operator associated to L from the space of measures toW1,p0(Ω) for all p ∈ [1, N/(N − 1)) together with fixed point arguments to solve problem (0.1) forany measure µ. Moreover, we provide explicit estimates of the solution in terms of the data. As anapplication, stability results are given. We also give conditions for the existence of W1,20-solutionsthrough the classic theory of monotone and coercive operators. In any case, we do not impose anysize restriction on µ and any sign condition on H.Fil: de Borbón, María Laura. Universidad Nacional de Cuyo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; ArgentinaFil: Ochoa, Pablo Daniel. Universidad Nacional de Cuyo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; ArgentinaHouse Book Science-casa Cartii Stiinta2024-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/231140de Borbón, María Laura; Ochoa, Pablo Daniel; Uniformly elliptic equations with concave growth in the gradient and measures; House Book Science-casa Cartii Stiinta; Fixed Point Theory; 25; 1; 2-2024; 43-601583-50222066-9208CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.math.ubbcluj.ro/~nodeacj/volumes/2024-No1/241-bor-och-0176-final-final.phpinfo:eu-repo/semantics/altIdentifier/doi/10.24193/fpt-ro.2025.1.04info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:10:46Zoai:ri.conicet.gov.ar:11336/231140instacron: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 10:10:46.362CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Uniformly elliptic equations with concave growth in the gradient and measures |
title |
Uniformly elliptic equations with concave growth in the gradient and measures |
spellingShingle |
Uniformly elliptic equations with concave growth in the gradient and measures de Borbón, María Laura Quasilinear elliptic equations Fixed point Green’s functions Weak solutions Uniqueness |
title_short |
Uniformly elliptic equations with concave growth in the gradient and measures |
title_full |
Uniformly elliptic equations with concave growth in the gradient and measures |
title_fullStr |
Uniformly elliptic equations with concave growth in the gradient and measures |
title_full_unstemmed |
Uniformly elliptic equations with concave growth in the gradient and measures |
title_sort |
Uniformly elliptic equations with concave growth in the gradient and measures |
dc.creator.none.fl_str_mv |
de Borbón, María Laura Ochoa, Pablo Daniel |
author |
de Borbón, María Laura |
author_facet |
de Borbón, María Laura Ochoa, Pablo Daniel |
author_role |
author |
author2 |
Ochoa, Pablo Daniel |
author2_role |
author |
dc.subject.none.fl_str_mv |
Quasilinear elliptic equations Fixed point Green’s functions Weak solutions Uniqueness |
topic |
Quasilinear elliptic equations Fixed point Green’s functions Weak solutions Uniqueness |
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 deal with quasilinear elliptic problems with measure data:Lw = H(x, w, ∇w) + µ in Ωw = 0 on ∂Ω,(0.1)where Lw := −div(A(x)∇w) with A = A(x) a bounded, coercive, and symmetric matrix field, theHamiltonian H has at most q-growth in the gradient for 0 < q < 1, and µ is any Radon measure.We employ the compactness of the Green operator associated to L from the space of measures toW1,p0(Ω) for all p ∈ [1, N/(N − 1)) together with fixed point arguments to solve problem (0.1) forany measure µ. Moreover, we provide explicit estimates of the solution in terms of the data. As anapplication, stability results are given. We also give conditions for the existence of W1,20-solutionsthrough the classic theory of monotone and coercive operators. In any case, we do not impose anysize restriction on µ and any sign condition on H. Fil: de Borbón, María Laura. Universidad Nacional de Cuyo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina Fil: Ochoa, Pablo Daniel. Universidad Nacional de Cuyo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina |
description |
We deal with quasilinear elliptic problems with measure data:Lw = H(x, w, ∇w) + µ in Ωw = 0 on ∂Ω,(0.1)where Lw := −div(A(x)∇w) with A = A(x) a bounded, coercive, and symmetric matrix field, theHamiltonian H has at most q-growth in the gradient for 0 < q < 1, and µ is any Radon measure.We employ the compactness of the Green operator associated to L from the space of measures toW1,p0(Ω) for all p ∈ [1, N/(N − 1)) together with fixed point arguments to solve problem (0.1) forany measure µ. Moreover, we provide explicit estimates of the solution in terms of the data. As anapplication, stability results are given. We also give conditions for the existence of W1,20-solutionsthrough the classic theory of monotone and coercive operators. In any case, we do not impose anysize restriction on µ and any sign condition on H. |
publishDate |
2024 |
dc.date.none.fl_str_mv |
2024-02 |
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/11336/231140 de Borbón, María Laura; Ochoa, Pablo Daniel; Uniformly elliptic equations with concave growth in the gradient and measures; House Book Science-casa Cartii Stiinta; Fixed Point Theory; 25; 1; 2-2024; 43-60 1583-5022 2066-9208 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/231140 |
identifier_str_mv |
de Borbón, María Laura; Ochoa, Pablo Daniel; Uniformly elliptic equations with concave growth in the gradient and measures; House Book Science-casa Cartii Stiinta; Fixed Point Theory; 25; 1; 2-2024; 43-60 1583-5022 2066-9208 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/https://www.math.ubbcluj.ro/~nodeacj/volumes/2024-No1/241-bor-och-0176-final-final.php info:eu-repo/semantics/altIdentifier/doi/10.24193/fpt-ro.2025.1.04 |
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 |
House Book Science-casa Cartii Stiinta |
publisher.none.fl_str_mv |
House Book Science-casa Cartii Stiinta |
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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