Die Maxwellgleichung mit wechselnden Randbedingungen (The Maxwell Equation with Mixed Boundary Conditions)

Details Die Maxwellgleichung mit wechselnden Randbedingungen (The Maxwell Equation with Mixed Boundary Conditions) Die Maxwellgleichung mit wechselnden Randbedingungen (The Maxwell Equation with Mixed Boundary Conditions)

2011-08-10

arxiv.org/abs/1108.2028v1

Mathematics

Analysis of PDEs

This is a preprint version of my dissertation (Dr. rer. nat.), submitted to the Fachbereich 6, Mathematik und Informatik, of t

Scientific paper

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.

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