Dirichlet–Neumann Problem for the Biharmonic Equation in Exterior Domains
Hovik A. Matevossian · Differential Equations · 2021
We study the uniqueness and the asymptotic expansion of the solution of the mixed Dirichlet–Neumann problem for the biharmonic equation in the exterior of a compact set under the assumption that the generalized solution of this problem has a finite Dirichlet integral with power-law weight with exponent $$a\in \mathbb {R}$$ . Depending on the value of the parameter $$a$$ , uniqueness (nonuniqueness) theorems are proved and exact formulas are found for the dimension of the linear solution space of the mixed Dirichlet–Neumann problem.