On solvability of the Neumann boundary value problem for a non-homogeneous polyharmonic equation in a ball

2013

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DOI 10.1186/1687-2770-2013-162
Data confidence 70 medium
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Abstract

In this work the Neumann boundary value problem for a non-homogeneous polyharmonic equation is studied in a unit ball. Necessary and sufficient conditions for solvability of this problem are found. To do this we first reduce the Neumann problem to the Dirichlet problem for a different non-homogeneous polyharmonic equation and then use the Green function of the Dirichlet problem. MSC: 35J40, 35J30, 35A01.