Regularity and singularities in polyhedral domains
The case of Laplace and Maxwell equations
Slides of a mini-course given on invitation at the Workshop ``Mathematical Topics in Electromagnetic Fields and Wave Propagation'' in the framawork of the ``Research Training Group Analysis, Simulation and Design of Nanotechnological Processes'' (University of Karlsruhe)
This is an introduction to singularities in corner domains for elliptic boundary value problems. The domains may have corners only, or edges only, or both (polyhedral domains). The operators are the Laplace operator with Dirichlet or Neumann boundary conditions, and the Maxwell system with PEC boundary conditions. The principal singularities of the Maxwell system are the gradients of the Laplace singularities with Dirichlet conditions. The Maxwell singularities are not in H1 if the domain has non-convex corners or edges.
Karlsruhe, April 7, 2008.
A complement about Helmholtz operator, April 21, 2008.