On increased stability in the continuation of the Helmholtz equation

dc.contributor.authorAralumallige, Deepak
dc.contributor.authorIsakov, Victor
dc.date.accessioned2013-07-25T15:20:29Z
dc.date.available2013-07-25T15:20:29Z
dc.date.issued2007-08
dc.descriptionClick on the DOI link to access the article (may not be free)en_US
dc.description.abstractIn this paper, we give analytical and numerical evidence of increasing stability in the Cauchy problem for the Helmholtz equation in the whole domain when frequency is growing. This effect depends upon the convexity properties of the surface where the Cauchy data are given. Proofs use previously obtained estimates in subdomains and the theory of Sobolev spaces: traces, embedding and interpolation theorems. The theory is illustrated by three-dimensional numerical examples. The results show that even in an acoustical frequency range the increase of resolution with growing frequency is quite dramatic. On the other hand, the resolution of continuation outside a unit sphere is decreasing.en_US
dc.description.versionPeer reviewed
dc.identifier.citationDeepak Aralumallige Subbarayappa and Victor Isakov. 2007. On increased stability in the continuation of the Helmholtz equation. Inverse Problems 23(4): 1689.en_US
dc.identifier.issn0266-5611
dc.identifier.issn1361-6420
dc.identifier.urihttp://dx.doi.org/10.1088/0266-5611/23/4/019
dc.identifier.urihttp://hdl.handle.net/10057/6051
dc.language.isoen_USen_US
dc.publisherIOP Publishingen_US
dc.relation.ispartofseriesInverse Problems;v.23
dc.rights.holderCopyright 2007 IOP PUBLISHING, LTD
dc.titleOn increased stability in the continuation of the Helmholtz equationen_US
dc.typeArticleen_US
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