On a Class of Wedge Diffraction Problems posted by Erhard Meister

Abstract

A class of canonical wedge diffraction problems for Helmholtz equations was formulated by E. Meister in 1986 and subsequently treated by an operator theoretical approach in various publications of his research group including two of the authors. Certain subclasses of those problems, recognized of being unsolved, are subject of the present paper. Some of them are now solved explicitly by refined operator theoretical and analytical methods, others are reduced to systems of equations which contain so-called convolution type operators with symmetry. By a new factorization approach those are proved to be Fredholm in certain (fractional) Sobolev spaces, sometimes with necessary compatibility conditions. Several of the associated operators are therefore explicitly inverted and a number of new problems can be recognized reflecting the challenges of the present state-of-the-art.KeywordsHelmholtz EquationRepresentation FormulaNormal TypeMinus TypeDiffraction ProblemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.