×

Wave diffraction problems with first and second kind conditions in a scale of spaces. (English) Zbl 1146.35334

Summary: A study for a class of plane wave diffraction problems by a union of two strips is presented in an operator-theoretical way. The class of problems is formulated in a setting of Bessel potential spaces which have a certain freedom as it concerns the smoothness indices. The main goal is to characterize the class of problems in view of its Fredholm properties. This means that we would like to obtain results on regularity (and data dependence) of the problems depending on the initial setting as well as on the boundary conditions which, in general, are of first and second kind. For this purpose, the problem is translated into a unique equation which is characterized by an operator. Therefore, knowledge of the regularity properties of this operator allows one to obtain the corresponding conclusions for this class of problems. The latter is obtained based on the construction of relations between convolution-type operators of different nature and acting between different kinds of spaces.

MSC:

35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J25 Boundary value problems for second-order elliptic equations
35Q60 PDEs in connection with optics and electromagnetic theory
47A53 (Semi-) Fredholm operators; index theories
47A68 Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
47F05 General theory of partial differential operators
PDFBibTeX XMLCite