Difference Quotients and Elliptic Mixed Boundary Problems of Second Order Moritz KassmannWolodymyr Madych 35J2535J6035B6560E05mixed boundary problemselliptic differential equationsEuler's equationdifference quotientsregularityFourier analysis 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. Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.2836 10.1512/iumj.2007.56.2836 en Indiana Univ. Math. J. 56 (2007) 1047 - 1082 state-of-the-art mathematics http://iumj.org/access/