Abstract
A generalization of the Farwig problem for a polyharmonic equation is considered, for which the uniqueness of solutions in unbounded domains (the exterior of a compact set, half-space, etc.) is studied under the assumption that the generalized solution of this problem has a finite Dirichlet integral with weight . Depending on the values of the parameter a, uniqueness (non-uniqueness) theorems are obtained and exact formulas are found for calculating the dimension of the space of solutions of these problems for a polyharmonic equation in the exterior of a compact set and in a half-space.
Disclosure statement
No potential conflict of interest was reported by the author(s).