A higher dimensional generalization of Hersch-Payne-Schiffer inequality for Steklov eigenvalues

作者：Yang, Liangwei; Yu, Chengjie^*

来源：Journal of Functional Analysis, 2017, 272(10): 4122-4130.

DOI：10.1016/j.jfa.2017.02.023

• Differential form
• Steklov eigenvalue
• Hodge-Laplacian

In this paper, we generalise the Hersch Payne Schiffer inequality for Steklov eigenvalues to higher dimensional case by extending the trick used by Hersch, Payne and Schiffer to higher dimensional manifolds. More precisely, we show that, for a compact oriented Riemannian manifold with boundary of dimension n, the multiplication of a Steklov eigenvalue for functions and a Steklov eigenvalue for differential (n -2)-forms can be controlled from above by a certain eigenvalue of the Laplacian operator on the boundary.

• 出版日期2017-5-15
• 单位汕头大学