Chandler-Wilde, Simon N.Simon N.Chandler-WildeLindner, MarkoMarkoLindner2021-10-252021-10-252008-12-01Journal of Integral Equations and Applications 20 (1): 13-48 (2008-12-01)http://hdl.handle.net/11420/10578We consider a class of boundary integral equations that arise in the study of strongly elliptic BVPs in unbounded domains of the form D = (x, z) ∈ Rn × R: z > f(x) where f: Rn → R is a sufficiently smooth bounded and continuous function. A number of specific problems of this type, for example, acoustic scattering problems, problems involving elastic waves and problems in potential theory, have been reformulated as second kind integral equations u + Ku = v in the space BC of bounded, continuous functions. Having recourse to the so-called limit operator method, we address two questions for the operator A = I + K under consideration, with an emphasis on the function space setting BC. Firstly, under which conditions is A a Fredholm operator, and, secondly, when is the finite section method applicable to A?. © 2008 Rocky Mountain Mathematics Consortium.en0897-3962200811348MathematikJournal Article10.1216/JIE-2008-20-1-13Other