DOIAbstract
AbstractIn Rn, n⩾2, we study the constructive and numerical solution of minimizing the energy relative to the Riesz kernel |x−y|α−n, where 1<α<n, for the Gauss variational problem, considered for finitely many compact, mutually disjoint, boundaryless (n−1)-dimensional C∞-manifolds Γℓ, ℓ∈L, each Γℓ being charged with Borel measures with the sign αℓ≔±1 prescribed. We show that the Gauss variational problem over an affine cone of Borel measures can alternatively be formulated as a minimum problem over an affine cone of surface distributions belonging to the Sobolev–Slobodetski space H−ε/2(Γ), where ε≔α−1 and Γ≔⋃ℓ∈LΓℓ. This allows the application of simple layer boundary integral operators on Γ and, hence, a penalty approximation. A correspondi...
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