To the theory of the Dirichlet and Neumann problems for strongly elliptic systems in Lipschitz domains

For strongly elliptic systems with Douglis-Nirenberg structure, we investigate the regularity of variational solutions to the Dirichlet and Neumann problems in a bounded Lipschitz domain. The solutions of the problems with homogeneous boundary conditions are originally defined in the simplest L-2-Sobolev spaces H-sigma. The regularity results are obtained in the potential spaces H-p(sigma) and Besov spaces B-p(sigma). In the case of second-order systems, the author's results obtained a year ago are strengthened. The Dirichlet problem with nonhomogeneous boundary conditions is considered with the use of Whitney arrays.