On solutions of the mixed Dirichlet-Steklov problem for the biharmonic equation in exterior domains

Abstract

We study the unique solvability of the mixed Dirichlet-Steklov problem for the biharmonic 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 uniqueness theorem or present exact formulas for the dimension of the solution space of the mixed Dirichlet-Steklov problem in the exterior of a compact set.