Properties of the solutions to the Monge-Ampère equation

Autores
Forzani, Liliana Maria; Maldonado, Diego
Año de publicación
2004
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider solutions to the equation detD2φ=μ when μ has a doubling property. We prove new geometric characterizations for this doubling property (by means of the so-called engulfing property) and deduce the quantitative behaviour of φ. Also, a constructive approach to the celebrated C1,β-estimates proved by L. Caffarelli is presented, settling one of the open questions posed by Villani (Amer. Math. Soc. 58 (2003)).
Fil: Forzani, Liliana Maria. 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: Maldonado, Diego. University Of Kansas, Lawrence;
Materia
MONGE-AMPÈRE EQUATION
MONGE-AMPÈRE MEASURE
SECTIONS OF CONVEX FUNCTIONS
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:11336/100624
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Properties of the solutions to the Monge-Ampère equationForzani, Liliana MariaMaldonado, DiegoMONGE-AMPÈRE EQUATIONMONGE-AMPÈRE MEASURESECTIONS OF CONVEX FUNCTIONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider solutions to the equation detD2φ=μ when μ has a doubling property. We prove new geometric characterizations for this doubling property (by means of the so-called engulfing property) and deduce the quantitative behaviour of φ. Also, a constructive approach to the celebrated C1,β-estimates proved by L. Caffarelli is presented, settling one of the open questions posed by Villani (Amer. Math. Soc. 58 (2003)).Fil: Forzani, Liliana Maria. 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: Maldonado, Diego. University Of Kansas, Lawrence; Pergamon-Elsevier Science Ltd2004-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/100624Forzani, Liliana Maria; Maldonado, Diego; Properties of the solutions to the Monge-Ampère equation; Pergamon-Elsevier Science Ltd; Journal Of Nonlinear Analysis; 57; 5-6; 5-2004; 815-8290362-546XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.na.2004.03.019info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:15:55Zoai:ri.conicet.gov.ar:11336/100624instacron: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 10:15:55.841CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Properties of the solutions to the Monge-Ampère equation
title Properties of the solutions to the Monge-Ampère equation
spellingShingle Properties of the solutions to the Monge-Ampère equation
Forzani, Liliana Maria
MONGE-AMPÈRE EQUATION
MONGE-AMPÈRE MEASURE
SECTIONS OF CONVEX FUNCTIONS
title_short Properties of the solutions to the Monge-Ampère equation
title_full Properties of the solutions to the Monge-Ampère equation
title_fullStr Properties of the solutions to the Monge-Ampère equation
title_full_unstemmed Properties of the solutions to the Monge-Ampère equation
title_sort Properties of the solutions to the Monge-Ampère equation
dc.creator.none.fl_str_mv Forzani, Liliana Maria
Maldonado, Diego
author Forzani, Liliana Maria
author_facet Forzani, Liliana Maria
Maldonado, Diego
author_role author
author2 Maldonado, Diego
author2_role author
dc.subject.none.fl_str_mv MONGE-AMPÈRE EQUATION
MONGE-AMPÈRE MEASURE
SECTIONS OF CONVEX FUNCTIONS
topic MONGE-AMPÈRE EQUATION
MONGE-AMPÈRE MEASURE
SECTIONS OF CONVEX FUNCTIONS
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 consider solutions to the equation detD2φ=μ when μ has a doubling property. We prove new geometric characterizations for this doubling property (by means of the so-called engulfing property) and deduce the quantitative behaviour of φ. Also, a constructive approach to the celebrated C1,β-estimates proved by L. Caffarelli is presented, settling one of the open questions posed by Villani (Amer. Math. Soc. 58 (2003)).
Fil: Forzani, Liliana Maria. 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: Maldonado, Diego. University Of Kansas, Lawrence;
description We consider solutions to the equation detD2φ=μ when μ has a doubling property. We prove new geometric characterizations for this doubling property (by means of the so-called engulfing property) and deduce the quantitative behaviour of φ. Also, a constructive approach to the celebrated C1,β-estimates proved by L. Caffarelli is presented, settling one of the open questions posed by Villani (Amer. Math. Soc. 58 (2003)).
publishDate 2004
dc.date.none.fl_str_mv 2004-05
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/11336/100624
Forzani, Liliana Maria; Maldonado, Diego; Properties of the solutions to the Monge-Ampère equation; Pergamon-Elsevier Science Ltd; Journal Of Nonlinear Analysis; 57; 5-6; 5-2004; 815-829
0362-546X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/100624
identifier_str_mv Forzani, Liliana Maria; Maldonado, Diego; Properties of the solutions to the Monge-Ampère equation; Pergamon-Elsevier Science Ltd; Journal Of Nonlinear Analysis; 57; 5-6; 5-2004; 815-829
0362-546X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.na.2004.03.019
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 Pergamon-Elsevier Science Ltd
publisher.none.fl_str_mv Pergamon-Elsevier Science Ltd
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
_version_ 1844614099403538432
score 13.070432

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