Integrability of derivations of classical solutions of Dirichlet's problem for an elliptic equation (Q762361)

The present work is concerned with integrability properties of derivatives of classical solutions of Dirichlet's problem for a linear second-order elliptic equation \(Lu=f\). With the aid of special weighted Hilbert spaces of locally square integrable functions, we determine the nature of singularities that f can have near the boundary, in order that such classical solutions are in the Sobolev space \(W^ 1\). By means of an example it is shown that the obtained result is exact.