Nonlinear multiplicative inequalities and estimates of gradients of solutions of elliptic equations (Q1101607)

The note is devoted to estimates in the metric of the spaces \(L^ p(\Omega)\), \(\Omega \subset R^{\ell}\), of the gradients of generalized solutions of the Dirichlet problem for the elliptic equations (- \(\sum^{\ell}_{k=1} \sum^{\ell}_{j=1}\partial /\partial x_ ka_{kj}\partial /\partial x_ j+\lambda)u=f.\)