On solutions of the mixed Dirichlet–Navier problem for the polyharmonic equation in exterior domains

Abstract

We study the unique solvability of the mixed Dirichlet–Navier problem for the polyharmonic equation in exterior domains under the assumption that a generalized solution of this problem has a bounded Dirichlet integral with weight |x|a. Depending on the value of the parameter a, we prove a uniqueness theorem or present exact formulas for the dimension of the solution space of the mixed Dirichlet–Navier problem in the exterior of a compact set.