Functional Analysis and Applications Seminar 

14/05/2004, 15:00 — 16:00 — Room P3.10, Mathematics Building
Ana Moura Santos, Instituto Superior Técnico, U.T. Lisboa

Regularity of Solutions to a Diffraction Problem with Oblique Derivatives on a Strip

We consider a boundary-transmission problem for the Helmholtz equation, in a Bessel potential space setting, which arises within the context of wave diffraction theory. The boundary under consideration consists of a strip, and certain conditions are assumed on it in the form of oblique derivatives. Those are of particular importance from the physical point of view in the context of materials involving non-homogeneous impedances in the boundary. The well-posedness of the problem is shown for a range of non-critical regularity orders of the Bessel potential spaces, which include the finite energy norm space. In addition, an operator normalization method is applied to the critical orders case.