publication . Article . Preprint . 2010

limit formulae and jump relations of potential theory in sobolev spaces

Raskop, Thomas; Grothaus, Martin;
Open Access
  • Published: 29 Jun 2010 Journal: GEM - International Journal on Geomathematics, volume 1, pages 51-100 (issn: 1869-2672, eissn: 1869-2680, Copyright policy)
  • Publisher: Springer Science and Business Media LLC
  • Country: Germany
Abstract
In this article we combine the modern theory of Sobolev spaces with the classical theory of limit formulae and jump relations of potential theory. Also other authors proved the convergence in Lebesgue spaces on ∂Σ for integrable functions, see for example Fichera (Ann Math Pura ed Appl Serie IV, Tomo 27, 1948) or Freeden and Kersten (The geodetic boundary value problem using the known surface of the Earth. Veroffentlichung des Geodatischen Instituts der RWTH Aachen, 29, 1980). The achievement of this paper is the L2(∂Σ) convergence for the weak derivatives of higher orders. Also the layer functions F are elements of Sobolev spaces and ∂Σ is a two dimensional sui...
Subjects
free text keywords: Modelling and Simulation, General Earth and Planetary Sciences, Jump, Sobolev space, Mathematics, Boundary value problem, Convergence (routing), Lp space, Potential theory, Mathematical analysis, Geomathematics, Submanifold, ddc:510
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