Closed-Form Inverses of the Weakly Singular and Hypersingular Operators on Disks

R. Hiptmair, C. Jerez-Hanckes, C. Urzúa-Torres

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We establish new explicit expressions and variational forms of boundary integral operators that provide the exact inverses of the weakly singular and hypersingular operators for - Δ on flat disks. We derive closed-form formulas for their singular kernels. We also show that the inverse of the weakly singular operator can be obtained by composing surface curl operators and the inverse of the hypersingular operator.

Original languageEnglish
Article number4
JournalIntegral Equations and Operator Theory
Volume90
Issue number1
DOIs
StatePublished - 1 Feb 2018
Externally publishedYes

Keywords

  • Boundary integral operators
  • Exact inverses
  • Projected spherical harmonics
  • Screens

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