Seminar in Numerical Analysis: Wolfgang Wendland (Universität Stuttgart)

Minimal energy problems with hypersingular Riesz potentials

The minimal energy problem for nonnegative charges on a closed surface Γ in R^3 goes back to C.F. Gauss in 1839. The corresponding Riesz kernel is then weakly singular on Γ. If one considers double layer potentials with dipole charges on Γ, the minimal energy problem then is based on hypersingular Riesz potentials in the form of Hadamard’s partie finie integral operators defining pseudodifferential operators of positive degree on smooth Γ. Existence and uniqueness results for the minimal energy problem and a corresponding boundary element method will be presented.

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