The outer oblique boundary problem of potential theory
- In this article we prove existence and uniqueness results for solutions to the outer oblique boundary problem for the Poisson equation under very weak assumptions on boundary, coefficients and inhomogeneities. Main tools are the Kelvin transformation and the solution operator for the regular inner problem, provided in [1]. Moreover we prove regularisation results for the weak solutions of both, the inner and the outer problem. We investigate the non-admissible direction for the oblique vector field, state results with stochastic inhomogeneities and provide a Ritz-Galerkinm approximation. The results are applicable to problems from Geomathematics, see e.g. [2] and [3].
Author: | Thomas Raskop, Martin Grothaus |
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URN: | urn:nbn:de:hbz:386-kluedo-16098 |
Series (Serial Number): | Schriften zur Funktionalanalysis und Geomathematik (43) |
Document Type: | Preprint |
Language of publication: | English |
Year of Completion: | 2009 |
Year of first Publication: | 2009 |
Publishing Institution: | Technische Universität Kaiserslautern |
Date of the Publication (Server): | 2009/07/13 |
Faculties / Organisational entities: | Kaiserslautern - Fachbereich Mathematik |
DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
Licence (German): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |