O. Chkadua, R. Duduchava, and D. Kapanadze

The Screen Type Dirichlet Boundary Value Problems for Anisotropic Pseudo-Maxwell's Equations

abstract:
We investigate the Dirichlet type boundary value problems for anisotropic pseudo-Maxwell's equations in screen type problems. It is shown that the problems with tangent Dirichlet traces are well-posed in tangent Sobolev spaces and they can equivalently be reduced to the Dirichlet boundary value problems in usual Sobolev spaces. Using the potential method and theory if pseudeodifferential equations the uniqieness and existence theorems are proved.
Asymptotic expansions of solutions near the screen edge are derived and used to establish the best Hölder smoothness for solutions.

Mathematics Subject Classification: 35J25, 35C15

Key words and phrases: Pseudo-Maxwell's equations, anisotropic media, uniqueness, existence, integral representation, potential theory, boundary pseudodifferential equation, asymptotics of solutions