On the polyharmonic Neumann problem in weighted spaces

Abstract

We study the unique (non-unique) solvability of the Neumann problem for the polyharmonic equation in unbounded domains under the assumption that a generalized solution of this problem has a bounded Dirichlet integral with weight . Depending on the value of the parameter a, we prove uniqueness (or non-uniqueness) theorems or present exact formulas for the dimension of the solution space of the Neumann problem in the exterior of a compact set and in a half space.