NONRADIATING SOURCES AND TRANSMISSION EIGENFUNCTIONS VANISH AT CORNERS AND EDGES

Emilia Blåsten*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We consider the inverse source problem of a fixed wavenumber: study properties of an acoustic source based on a single far- or near-field measurement. We show that nonradiating sources having a convex or nonconvex corner or edge on their boundary must vanish there. The same holds true for smooth enough transmission eigenfunctions. The proof is based on an energy identity from the enclosure method and the construction of a new type of planar complex geometrical optics solution whose logarithm is a branch of the square root. The latter allows us to deal with nonconvex corners and edges.

Original languageEnglish
Pages (from-to)6255-6270
Number of pages16
JournalSIAM Journal on Mathematical Analysis
Volume50
Issue number6
DOIs
Publication statusPublished - 2018
MoE publication typeA1 Journal article-refereed

Keywords

  • inverse source problem
  • nonradiating
  • corner scattering
  • complex geometrical optics
  • interior transmission eigenfunction
  • INVERSE CONDUCTIVITY PROBLEM
  • HELMHOLTZ-EQUATION
  • UNIQUENESS
  • SCATTERING
  • RECONSTRUCTION

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