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Kernel and eigenfunction estimates for some second order elliptic operators

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorOUHABAZ, El Maati
hal.structure.identifierDepartment of Information Engineering, Electrical Engineering and Applied Mathematics [DIEM]
dc.contributor.authorRHANDI, Abdelaziz
dc.date.accessioned2024-04-04T02:18:05Z
dc.date.available2024-04-04T02:18:05Z
dc.date.created2011
dc.date.issued2012
dc.identifier.issn0022-247X
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189281
dc.description.abstractEnFor a potential V such that V (x) |x|α with α > 2 we prove that the heat kernel kt (x, y) associated to the uniformly elliptic operator A =− nj ,k=1 ∂k(a jk∂ j ) + V satisfies the estimate kt (x, y) Ce−μ0tect−b e− 2 √ θ α+2 |x|1+α2 |x|α4 +n−1 2 e− 2 √ θ α+2 |y|1+α2 |y|α4 +n−1 2 for large x, y ∈ Rn and all t > 0. Here 0 < θ 1 is an appropriate constant, b > α+2 α−2 and μ0 is the first eigenvalue of A. We also obtain an estimate for large |x| of the eigenfunctions of A. ©
dc.language.isoen
dc.publisherElsevier
dc.subject.enHeat kernels Schrödinger operators Eigenfunctions Log-Sobolev inequality
dc.title.enKernel and eigenfunction estimates for some second order elliptic operators
dc.typeArticle de revue
dc.identifier.doi10.1016/j.jmaa.2011.09.045
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
bordeaux.journalJournal of Mathematical Analysis and Applications
bordeaux.page799-806
bordeaux.volume387
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue2
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00992219
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00992219v1
bordeaux.COinSctx_ver=Z39.88-2004&amp;rft_val_fmt=info:ofi/fmt:kev:mtx:journal&amp;rft.jtitle=Journal%20of%20Mathematical%20Analysis%20and%20Applications&amp;rft.date=2012&amp;rft.volume=387&amp;rft.issue=2&amp;rft.spage=799-806&amp;rft.epage=799-806&amp;rft.eissn=0022-247X&amp;rft.issn=0022-247X&amp;rft.au=OUHABAZ,%20El%20Maati&amp;RHANDI,%20Abdelaziz&amp;rft.genre=article


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