IUMJ

Title: Difference Quotients and Elliptic Mixed Boundary Problems of Second Order

Authors: Moritz Kassmann and W. R. Madych

Issue: Volume 56 (2007), Issue 3, 1047-1082

Abstract:

This article concerns regularity of solutions $u$ of second order elliptic mixed boundary value problems in the upper halfspace $\mathbb{R}^n_+$. Conditions on the boundary data which ensure that $u$ be in the smoothness class $\mathcal{B}^{s}_{2,infty}(\mathbb{R}^n_+)$, $s \leq \frac32$, 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.