Beltrami equations with coefficient in the Sobolev space W1,p.
We study the behaviour of weak solutions (as well as their gradients) of boundary value problems for quasi-linear elliptic divergence equations in domains extending to infinity along a cone.
Let -div be a second order elliptic operator with real, symmetric, bounded measurable coefficients on or on a bounded Lipschitz domain subject to Dirichlet boundary condition. For any fixed , a necessary and sufficient condition is obtained for the boundedness of the Riesz transform on the space. As an application, for , we establish the boundedness of Riesz transforms on Lipschitz domains for operators with coefficients. The range of is sharp. The closely related boundedness of ...