The regularity problem in domains with lower dimensional boundaries

In the present paper we establish solvability of Regularity boundary value problem in domains with lower dimensional boundaries (flat and Lipschitz) for operators whose coefficients exhibit small oscillations analogous to Dahlberg-Kenig-Pipher condition. The proof follows classical strategy showing bounds on square function non-tangential maximal function. key novelty difficulty this setting is presence multiple derivatives. To solve it, consider a cylindrical system derivatives new estimates “angular derivatives”.