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hal.structure.identifierCentre de Mathématiques Laurent Schwartz [CMLS]
dc.contributor.authorCarrapatoso, Kleber
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorDolbeault, Jean
HAL ID: 87
ORCID: 0000-0003-4234-2298
hal.structure.identifierLaboratoire de Mathématiques Jean Leray [LMJL]
dc.contributor.authorHérau, Frédéric
HAL ID: 746014
ORCID: 0000-0001-9832-7105
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorMischler, Stéphane
hal.structure.identifierDepartment of Pure Mathematics and Mathematical Statistics [DPMMS]
dc.contributor.authorMouhot, Clément
HAL ID: 1892
dc.date.accessioned2021-10-29T12:47:59Z
dc.date.available2021-10-29T12:47:59Z
dc.date.issued2020
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22119
dc.language.isoenen
dc.subjectKorn inequalityen
dc.subjectweighted Poincaré inequalityen
dc.subjectPoincaré-Korn inequalityen
dc.subjectLions' lemmaen
dc.subjectWitten-Laplace operatoren
dc.subjectGrad's numberen
dc.subject.ddc515en
dc.titleWeighted Korn and Poincaré-Korn inequalities in the Euclidean space and associated operatorsen
dc.typeDocument de travail / Working paper
dc.description.abstractenWe prove functional inequalities on vector fields on the Euclidean space when it is equipped with a bounded measure that satisfies a Poincaré inequality, and study associated self-adjoint operators. The weighted Korn inequality compares the differential matrix, once projected orthogonally to certain finite-dimensional spaces, with its symmetric part and, in an improved form of the inequality, an additional term. We also consider Poincaré-Korn inequalities for estimating a projection of the vector field by the symmetric part of the differential matrix and zeroth-order versions of these inequalities obtained using the Witten-Laplace operator. The constants depend on geometric properties of the potential and the estimates are quantitative and constructive. These inequalities are motivated by kinetic theory and related with the Korn inequality (1906) in mechanics, on a bounded domain.en
dc.publisher.cityParisen
dc.identifier.citationpages20en
dc.relation.ispartofseriestitleCahier de recherche du CEREMADEen
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-03059166en
dc.subject.ddclabelAnalyseen
dc.identifier.citationdate2020
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2021-10-29T12:41:24Z
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