Lp-theory of boundary integral operators for domains with unbounded smooth boundary

Abstract

AbstractThe paper is devoted to the ${L^{p}}$-theory of boundary integral operators for boundary value problems described by anisotropic Helmholtz operators with variable coefficients in unbounded domains with unbounded smooth boundary. We prove the invertibility of boundary integral operators for Dirichlet and Neumann problems in the Bessel-potential spaces ${H^{s,p}(\partial D)}$, ${p\in(1,\infty)}$, and the Besov spaces ${B_{p,q}^{s}(\partial D)}$, ${p,q\in[1,\infty]}$. We prove also the Fredholmness of the Robin problem in these spaces and give the index formula.