$L^p$ polyharmonic Robin problems on Lipschitz domains

Abstract

In this paper, we study a class of boundary value problems (BVPs) with Robin conditions in some $L^p$ spaces for polyharmonic equation on Lipschitz domains. Utilizing polyharmonic fundamental solutions, these Robin BVPs are solved by the method of layer potentials. The crucial ingedients of our approach are the classical single layer potential and its higher order analog (which are called multi-layer $S$-potentials), and the main results generalize ones of second order (Laplacian) case to higher order (polyharmonic) case.