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Paralinearization of the Dirichlet to Neumann operator

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorMETIVIER, Guy
hal.structure.identifierLaboratoire de Mathématiques d'Orsay [LMO]
dc.contributor.authorALAZARD, Thomas
dc.date.accessioned2024-04-04T02:23:03Z
dc.date.available2024-04-04T02:23:03Z
dc.date.created2009
dc.date.issued2009
dc.identifier.issn0360-5302
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189696
dc.description.abstractEnThis paper is concerned with {\em a priori\/} $C^\infty$ regularity for three-dimensional doubly periodic travelling gravity waves whose fundamental domain is a symmetric diamond. The existence of such waves was a long standing open problem solved recently by Iooss and Plotnikov. The main difficulty is that, unlike conventional free boundary problems, the reduced boundary system is not elliptic for three-dimensional pure gravity waves, which leads to small divisors problems. Our main result asserts that sufficiently smooth diamond waves which satisfy a diophantine condition are automatically~$C^\infty$. In particular, we prove that the solutions defined by Iooss and Plotnikov are $C^\infty$. Two notable technical aspects are that (i) no smallness condition is required and (ii) we obtain an exact paralinearization formula for the Dirichlet to Neumann operator.
dc.language.isoen
dc.publisherTaylor & Francis
dc.title.enParalinearization of the Dirichlet to Neumann operator
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
bordeaux.journalCommunications in Partial Differential Equations
bordeaux.page1634--1704
bordeaux.volume34
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00777059
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00777059v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Communications%20in%20Partial%20Differential%20Equations&rft.date=2009&rft.volume=34&rft.spage=1634--1704&rft.epage=1634--1704&rft.eissn=0360-5302&rft.issn=0360-5302&rft.au=METIVIER,%20Guy&ALAZARD,%20Thomas&rft.genre=article


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