Existence and uniqueness of the scattering solutions in the exterior of rough domains

Details Existence and uniqueness of the scattering solutions in the exterior of rough domains Existence and uniqueness of the scattering solutions in the exterior of rough domains

1999-11-28

arxiv.org/abs/math-ph/9911046v1

Physics

Mathematical Physics

Scientific paper

Existence and uniqueness of the scattering solutions is proved for a class of bounded rough obstacles which is much larger than the class of Lipschitz obstacles. Integral equations method is not used. The approach is based on the representation theorem for selfadjoint operators via closed symmetric quadratic forms and on the limiting absorption principles. For the Dirichlet boundary condition no assumptions on the smoothness of the boundary are needed, for the Neumann boundary condition and the Robin boundary condition some assumptions on the smoothness of the boundary are needed.

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