Local Regularity Results for Second Order Elliptic Systems on Lipschitz Domains
Local Regularity Results for Second Order Elliptic Systems on Lipschitz Domains
For a class of strongly elliptic, second order systems $L$ with rough coefficients on a Lipschitz domain $\Omega$, we show that if $Lu=0$ on $\Omega$ and $u$ vanishes on an open subset of the boundary, then weak a priori hypotheses on the nontangential maximal function of $u$ lead to strong …