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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.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorEsteban, Maria J.
HAL ID: 738381
ORCID: 0000-0003-1700-9338
hal.structure.identifierSchool of Mathematics - Georgia Institute of Technology
dc.contributor.authorLoss, Michael
dc.date.accessioned2020-04-14T10:27:01Z
dc.date.available2020-04-14T10:27:01Z
dc.date.issued2018
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/20630
dc.language.isoenen
dc.subjectSymmetryen
dc.subjectsymmetry breakingen
dc.subjectinterpolation inequalitiesen
dc.subjectCaffarelli-Kohn-Niren-berg inequalitiesen
dc.subjectoptimal constantsen
dc.subjectrigidity resultsen
dc.subjectfast diffusion equationen
dc.subjectcarré du champen
dc.subjectbifurcationen
dc.subjectinstability.en
dc.subject.ddc515en
dc.titleSymmetry and symmetry breaking: rigidity and flows in elliptic PDEsen
dc.typeCommunication / Conférence
dc.description.abstractenThe issue of symmetry and symmetry breaking is fundamental in all areas of science. Symmetry is often assimilated to order and beauty while symmetry breaking is the source of many interesting phenomena such as phase transitions, instabilities, segregation, self-organization, etc. In this contribution we review a series of sharp results of symmetry of nonnegative solutions of nonlinear elliptic differential equation associated with minimization problems on Euclidean spaces or manifolds. Nonnegative solutions of those equations are unique, a property that can also be interpreted as a rigidity result. The method relies on linear and nonlinear flows which reveal deep and robust properties of a large class of variational problems. Local results on linear instability leading to symmetry breaking and the bifurcation of non-symmetric branches of solutions are reinterpreted in a larger, global, variational picture in which our flows characterize directions of descent.en
dc.identifier.citationpages2261-2285en
dc.relation.ispartoftitleInternational Congress of Mathematicians 2018en
dc.relation.ispartofpublnameWorld Scientificen
dc.relation.ispartofpublcitySingaporeen
dc.relation.ispartofpages13en
dc.subject.ddclabelAnalyseen
dc.relation.ispartofisbn978-981-327-287-3;978-981-327-288-0en
dc.relation.conftitleInternational Congress of Mathematics - ICM 2018en
dc.relation.confdate2018-05
dc.relation.confcityRio de Janeiroen
dc.relation.confcountryBrazilen
dc.relation.forthcomingnonen
dc.identifier.doi10.1142/9789813272880_0138en
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewednonen
dc.relation.Isversionofjnlpeerreviewednonen
dc.date.updated2020-04-14T10:23:22Z
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