Mixed type boundary value problems for polymetaharmonic equations

In the paper we consider three-dimensional Riquier-type and classical mixed boundary value problems for the polymetaharmonic equation (Delta + k(1)(2))(Delta + k(2)(2))u = 0. We investigate these problems by means of the potential method and the theory of pseudodifferential equations. We prove the existence and uniqueness theorems in Sobolev-Slobodetskii spaces, analyse the asymptotic properties of solutions and establish the best Holder smoothness results for solutions.