Abstract

We study the unique solvability of the mixed biharmonic problem with the Steklov-type and Farwig conditions on the boundary in the exterior of a compact set under the assumption that generalized solutions of this problem has a bounded Dirichlet integral with weight \(|x|^{a}\). Depending on the value of the parameter \(a\), we obtained uniqueness (non-uniqueness) theorems of this problem or present exact formulas for the dimension of the space of solutions.

中文翻译：

---

Steklov型和Farwig边界条件的双调和问题

摘要

我们在紧要集的广义解具有权重\（| x | ^的有界Dirichlet积分的假设下，研究紧集外部边界上具有Steklov型和Farwig条件的混合双调和问题的独特可解性{a} \）。根据参数\（a \）的值，我们获得了该问题的唯一性（非唯一性）定理，或给出了解决方案空间维数的精确公式。