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