Mathematics – Analysis of PDEs
Scientific paper
2011-05-20
Analysis (Munich), 27, (2007), 425-464
Mathematics
Analysis of PDEs
Key Words: exterior boundary value problems, Maxwell's equations, variable coefficients, electro-magnetic theory, electro-magn
Scientific paper
We develop a solution theory for a generalized electro-magneto static Maxwell system in an exterior domain with anisotropic coefficients converging at infinity with a certain rate towards the identity. Our main goal is to treat right hand side data from some polynomially weighted Sobolev spaces and obtain solutions which are up to a finite sum of special generalized spherical harmonics in another appropriately weighted Sobolev space. As a byproduct we prove a generalized spherical harmonics expansion suited for Maxwell equations. In particular, our solution theory will allow us to give meaning to higher powers of a special static solution operator. Finally we show, how this weighted static solution theory can be extended to handle inhomogeneous boundary data as well. This paper is the second one in a series of three papers, which will completely reveal the low frequency behavior of solutions of the time-harmonic Maxwell equations.
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