Lp polyharmonic Robin problems on Lipschitz domains
Weifeng Li, Pei Dang, Zhihua Du, Guoan Guo, Yumei Li · Complex Variables and Elliptic Equations · 2019
In this paper, we study a class of boundary value problems (BVPs) with Robin conditions in some Lp 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.