Local inverse estimates for non-local boundary integral operators

Abstract

We prove local inverse-type estimates for the four non-local boundary integral operators associated with the Laplace operator on a bounded d-dimensional Lipschitz domain Omega for d >= 2 with piecewise smooth boundary. For piecewise polynomial ansatz spaces and d = 2 or 3, the inverse estimates are explicit in both the local mesh width and the approximation order. An application to efficiency estimates in a posteriori error estimation in boundary element methods is given.