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Abstract <p>The unique solvability of the Farwig problem for the biharmonic equation in a half-space is studied under the assumption that the generalized solutions of this problem have a finite weighted Dirichlet integral. Depending on the value of the weight parameter, uniqueness theorems are proved or exact formulas are given for calculating the dimension of the solution space of the Farwig biharmonic problem in a half-space.</p>

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Farwig Problem for the Biharmonic Equation in a Half-Space

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • Hovik A. Matevossian

摘要

Abstract

The unique solvability of the Farwig problem for the biharmonic equation in a half-space is studied under the assumption that the generalized solutions of this problem have a finite weighted Dirichlet integral. Depending on the value of the weight parameter, uniqueness theorems are proved or exact formulas are given for calculating the dimension of the solution space of the Farwig biharmonic problem in a half-space.