Geymonat extended Gurtin’s result on Beltrami’s completeness to L2-case. The first objective of this paper is to generalize Geymonat’s result to Lp-case with tangential and normal boundary conditions. Maggiani et al. proposed an extension of Beltrami’s-type decomposition for symmetric matrix fields in 𝕃sp(Ω) when Ω is simply connected domain and of class 𝒞∞. The second objective of this paper is to present more extensions of the above decomposition when the domain Ω is only of class 𝒞1,1 and not necessarily simply connected. The third objective of this paper is to use the previous characterizations of matrix fields to solve some variants of the bi-Laplacian problem.

中文翻译：

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Beltrami 对 𝕃p 对称矩阵场的完备性

Geymonat 将 Gurtin 关于贝尔特拉米完整性的结果扩展到大号2-案子。本文的第一个目标是将 Geymonat 的结果推广到大号p- 具有切向和法向边界条件的情况。马贾尼等。提出了对对称矩阵场的贝尔特拉米类型分解的扩展𝕃sp(Ω)什么时候Ω是简单连通域和类𝒞∞. 本文的第二个目标是在定义域时对上述分解提出更多扩展Ω只是类𝒞1,1不一定是简单的连接。本文的第三个目标是利用矩阵场的先前表征来解决双拉普拉斯问题的一些变体。