An Operator Approach for an Oblique Derivative
Boundary-Transmission Problem
We consider a boundary-transmission problem for the Helmholtz
equation in a Bessel potential space setting. The boundary is a
strip of infinite extent and certain boundary conditions are
assumed on it in the form of oblique derivatives. The problem has
an interpretation within the context of diffraction theory and we
discuss the relevance of oblique derivatives boundary conditions.
Operator theoretical methods are used to deal with the problem and,
consequently, several convolution type operators are constructed
and "associated" to the problem. We also compare these results with
the previous construction of operators in the half-plane case. At
the end, the well-posedness of the problem is shown for orders of
the Bessel potential space near to that of the finite energy norm.
07/03/2003, 14:00 — 15:00 — Sala P3.10, Pavilhão de Matemática
