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Screen‐type boundary value problems for polymetaharmonic equations
Author(s) -
Chkadua G.
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2602
Subject(s) - mathematics , uniqueness , sobolev space , type (biology) , smoothness , boundary value problem , mathematical analysis , dirichlet distribution , dirichlet problem , dirichlet boundary condition , biology , ecology
In this paper, we consider the three‐dimensional Riquier‐type and Dirichlet‐type screen boundary value problems for the polymetaharmonic equationΔ + k 1 2Δ + k 2 2u = 0 with real wave numbers k 1 and k 2 . 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.