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 harmonicsMathematics Subject Classification
Primary 45P05 31A10 65R20 Secondary 65N38References
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