ISSN:
0170-4214
Keywords:
Mathematics and Statistics
;
Applied Mathematics
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
The paper gives a proof, valid for a large class of bounded domains, of the following compactness statements: Let G be a bounded domain, β be a tensor-valued function on G satisfying certain restrictions, and let {n} be a sequence of vector-valued functions on G where the L2-norms of {n}, {curl n}, and {div(β n)} are bounded, and where all n either satisfy x n = 0 or (β Fn) = 0 at the boundary ∂G of G ( = normal to ∂G): then {n} has a L2-convergent subsequence. The first boundary condition is satisfied by electric fields, the second one by magnetic fields at a perfectly conducting boundary ∂G if β is interpreted as electric dielectricity ∊ or as magnetic permeability μ, respectively.These compactness statements are essential for the application of abstract scattering theory to the boundary value problem for Maxwell's equations.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/mma.1670020103
