The BMO-Dirichlet problem for elliptic systems in the upper half-space and quantitative characterizations of VMO
The BMO-Dirichlet problem for elliptic systems in the upper half-space and quantitative characterizations of VMO
We prove that for any homogeneous, second order, constant complex coefficient elliptic system $L$, the Dirichlet problem in $\mathbb{R}^{n}_{+}$ with boundary data in BMO is well-posed in the class of functions $u$ with $d\mu_u(x',t):=|\nabla u(x',t)|^2\,t\,dx'dt$ being a Carleson measure. We establish a Fatou type theorem guaranteeing the existence of the …