Geoelectrical conductivity problems on unbounded domains

  • This paper deals with the electrical conductivity problem in geophysics. It is formulated as an elliptic boundary value problem of second order for a large class of bounded and unbounded domains. A special boundary condition, the so called "Complete Electrode Model", is used. Poincaré inequalities are formulated and proved in the context of weighted Sobolev spaces, leading to existence and uniqueness statements for the boundary value problem. In addition, a parameter-to-solution operator arising from the inverse conductivity problem in medicine (EIT) and geophysics is investigated mathematically and is shown to be smooth and analytic.

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Author:Michael Lukaschewitsch
Series (Serial Number):NLD Preprints (paper 045)
Document Type:Preprint
Year of Completion:1998
Publishing Institution:Universität Potsdam
Release Date:2007/07/13
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Zentrale und wissenschaftliche Einrichtungen / Interdisziplinäres Zentrum für Dynamik komplexer Systeme
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik