Die Maxwellgleichung mit wechselnden Randbedingungen (The Maxwell Equation with Mixed Boundary Conditions)
Abstract
In the thesis at hand we give a comprehensive discussion of basic problems for generalized Maxwell equations with mixed boundary conditions using the calculus of alternating differential forms on Riemannian manifolds of arbitrary dimension. We prove compactness results, Hodge decompositions and Poincare type estimates. For the case of 'full' boundary conditions we present trace and extension theorems, regularity theory as well as a detailed solution theory for static Maxwell problems.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2011
- DOI:
- 10.48550/arXiv.1108.2028
- arXiv:
- arXiv:1108.2028
- Bibcode:
- 2011arXiv1108.2028K
- Keywords:
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- Mathematics - Analysis of PDEs;
- Mathematical Physics;
- Mathematics - Differential Geometry;
- Mathematics - Functional Analysis
- E-Print:
- This is a preprint version of my dissertation (Dr. rer. nat.), submitted to the Fachbereich 6, Mathematik und Informatik, of the University of Essen, Germany, in August 1999. The thesis was published by Shaker (Aachen, Germany) in January 2000