We consider the Neumann problem in a theory of plane micropolar elasticity incorporating micropolar surface effects. The incorporation of surface elasticity utilizes the Eremeyev–Lebedev–Altenbach shell model, leading to a set of second-order boundary conditions describing the separate micropolar elasticity of the surface. The Neumann problem is of particular interest, since the question of solvability is complicated by the fact that the corresponding systems of homogeneous singular integral equations admit nontrivial solutions that affect the solvability of both the interior and exterior Neumann boundary value problems. We overcome this difficulty by constructing integral representations of the solutions based on specifically constructed auxiliary matrix functions leading to uniqueness and existence theorems in appropriate classes of smooth matrix functions.

中文翻译：

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具有微极表面效应的微极弹性固体平面变形中的诺依曼问题

我们在包含微极表面效应的平面微极弹性理论中考虑诺依曼问题。表面弹性的结合利用 Eremeyev-Lebedev-Altenbach 壳模型，导致一组描述表面单独微极弹性的二阶边界条件。Neumann 问题特别令人感兴趣，因为可解性问题由于齐次奇异积分方程的相应系统允许影响内部和外部 Neumann 边值问题的可解性的非平凡解这一事实而变得复杂。