Abstract
Abstract In the paper we consider three-dimensional Riquier-type and classical mixed boundary value problems for the polymetaharmonic equation ( Δ + k 1 2 ) ( Δ + k 2 2 ) u = 0 ${(\Delta+k^{2}_{1})(\Delta+k^{2}_{2})u=0}$ . 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 Hölder smoothness results for solutions.
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