Riesz minimal energy problems on Ck−1,1-manifolds

Harbrecht, Helmut and Wendland, Wolfgang L. and Zorii, Natalia. (2014) Riesz minimal energy problems on Ck−1,1-manifolds. Mathematische Nachrichten, Vol. 287, H. 1. pp. 48-69.

Full text not available from this repository.

Official URL: http://edoc.unibas.ch/dok/A6212117

Downloads: Statistics Overview


In $mathbb R^n$, $ngeqslant 2$, we study the constructive and numerical solution of minimizing the energy relative to the Riesz kernel $|{bf x}-{bf y}|^{alpha-n}$, where $1>alpha(alpha-1)/2$, each $Gamma_ell$ being charged with Borel measures with the sign $alpha_ell:=pm1$ prescribed. We show that the Gauss variational problem over a convex set of Borel measures can alternatively be formulated as a minimum problem over the corresponding set of surface distributions belonging to the Sobolev-Slobodetski space $H^{-{varepsilon}/{2}}(Gamma)$, where $varepsilon:=alpha-1$ and $Gamma:=bigcup_{ellin L}Gamma_ell$. An equivalent formulation leads in the case of two manifolds to a nonlinear system of boundary integral equations involving simple layer potential operators on~$Gamma$. A corresponding numerical method is based on the Galerkin-Bubnov discretization with piecewise constant boundary elements. Wavelet matrix compression is applied to sparsify the system matrix. Numerical results are presented to illustrate the approach.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
UniBasel Contributors:Harbrecht, Helmut
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Wiley-VCH Verlag
Note:Publication type according to Uni Basel Research Database: Journal article
Last Modified:31 Jan 2014 09:51
Deposited On:31 Jan 2014 09:51

Repository Staff Only: item control page