Difference Quotients and Elliptic Mixed Boundary Problems of Second Order

Abstract

. This article concerns regularity of solutions u of second order elliptic mixed boundary value problems in the upper halfspace R n + . Conditions on the boundary data which ensure that u be in the smoothness class B s 2,∞ (R n + ), s ≤ 2 3, are established. Linear operators with variable coefficients and certain nonlinear operators are studied. The novel feature of the techniques developed involves results on the L 2 smoothness of distributions.