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
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/231140
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/231140
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling 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 Técnicas2025-10-22T11:40:43Zoai: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:34982025-10-22 11:40:43.824CONICET 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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score 12.982451

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