We prove a regularity result for the Poisson problem ΓDu ΒΌ f , uj oP ΒΌ g on a polyhedral domain P & R 3 using the Babus Λka-Kondratiev spaces K m a Γ°PΓ. These are weighted Sobolev spaces in which the weight is given by the distance to the set of edges [4,33]. In particular, we show that there is no
Weighted regularization of Maxwell equations in polyhedral domains
β Scribed by Martin Costabel; Monique Dauge
- Publisher
- Springer-Verlag
- Year
- 2002
- Tongue
- English
- Weight
- 309 KB
- Volume
- 93
- Category
- Article
- ISSN
- 0029-599X
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π SIMILAR VOLUMES
The solution of Maxwell's equations in a non-convex polyhedral domain is less regular than in a smooth or convex polyhedral domain. In this paper we show that this solution can be decomposed into the orthogonal sum of a singular part and a regular part, and we give a characterization of the singular
Nonlinear elliptic equations with p-structure on non-convex polyhedral domains under homogeneous Dirichlet boundary values are considered. Global regularity in fractional order Nikolskij and Sobolev spaces is proved.
## Abstract The solution of the Dirichlet problem relative to an elliptic operator in a polyhedron has a complex singular behaviour near edges and vertices. Here we show that this solution and its conormal derivative have a global regularity in appropriate weighted Sobolev spaces. We also investiga