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

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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 \(-\Delta \) 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.

Keywords

Boundary integral operators Screens Exact inverses Projected spherical harmonics 

Mathematics Subject Classification

Primary 45P05 31A10 65R20 Secondary 65N38 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • R. Hiptmair
    • 1
  • C. Jerez-Hanckes
    • 2
  • C. Urzúa-Torres
    • 1
  1. 1.Seminar for Applied MathematicsETH ZurichZurichSwitzerland
  2. 2.School of EngineeringPontificia Universidad Católica de ChileMaculChile

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