On analytic continuability of the missing Cauchy datum for Helmholtz boundary problems

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Abstract

We relate the domains of analytic continuation of Dirichlet and Neumann boundary data for Helmholtz problems in two or more independent variables. The domains are related à priori, locally and explicitly in terms of complex polyrectangular neighbourhoods of planar pieces of the boundary. To this end we identify and characterise a special subspace of the standard pseudodifferential operators with real-analytic symbols. The result is applicable in the estimation of the domain of analytic continuation of solutions across planar pieces of the boundary.
Original languageEnglish
JournalProceedings of the American Mathematical Society
Volume143
Issue number4
Pages (from-to)1515-1530
Number of pages16
ISSN0002-9939
DOIs
Publication statusPublished - 2015

Bibliographical note

Communicated by Richard Rochberg

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