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Screen‐type boundary value problems for polymetaharmonic equations

In this paper, we consider the three‐dimensional Riquier‐type and Dirichlet‐type screen boundary value problems for the polymetaharmonic equation Δ + k12 Δ + k22 u = 0 with real wave numbers k1 and k2. We investigate these problems by means of the potential method and the theory of pseudodifferential equations, prove the existence and uniqueness of solutions in Sobolev–Slobodetski spaces, and on the basis of asymptotic analysis, we establish the best Hölder smoothness results for solutions. Copyright © 2012 John Wiley & Sons, Ltd.