Mixed Problems in a Lipschitz Domain for Strongly Elliptic Second-Order Systems

We consider mixed problems for strongly elliptic second-order systems in a bounded domain with Lipschitz boundary in the space R(n). For such problems, equivalent equations on the boundary in the simplest L(2)-spaces H(s) of Sobolev type are derived, which permits one to represent the solutions via surface potentials. We prove a result on the regularity of solutions in the slightly more general spaces H(p)(s) of Bessel potentials and Besov spaces B(p)(s). Problems with spectral parameter in the system or in the condition on a part of the boundary are considered, and the spectral properties of the corresponding operators, including the eigenvalue asymptotics, are discussed.