微分流形上微分形式的Gaffney不等式新证明：Kozono-Yanagisawa方法的变分方法
A new proof of the Gaffney's inequality for differential forms on manifolds-with-boundary: the variational approach à la Kozono--Yanagisawa
AI总结：
本文通过变分方法和Bochner技术，为微分流形上微分形式的Gaffney不等式提供新证明。
摘要：
设$(\mathcal{M},g_0)$为带有边界的紧致黎曼流形。我们通过Kozono-Yanagisawa方法的变分方法，给出了微分流形上微分形式在边界值空间中经典Gaffney不等式的新证明，结合基于Bochner技术的全局计算。
英文摘要：
Let $(\mathcal{M},g_0)$ be a compact Riemannian manifold-with-boundary. We present a new proof of the classical Gaffney's inequality for differential forms in boundary value spaces over $\mathcal{M}$, via the variational approach à la Kozono--Yanagisawa [$L^r$-variational inequality for vector fields and the Helmholtz--Weyl decomposition in bounded domains, Indiana Univ. Math. J. 58 (2009), 1853--1920] combined with global computations based on the Bochner's technique.
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