Abstract
We prove a Payne–Rayner type inequality for the first eigenfunction of the Laplacian with Robin boundary condition on any compact minimal surface with boundary in \({\mathbb{R}^N}\). We emphasize that no topological condition is necessary on the boundary.
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F. Takahashi acknowledges the support by JSPS Grant-in-Aid for Scientific Research (C), No. 20540216.
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Takahashi, F., Uegaki, A. A Payne–Rayner Type Inequality for the Robin Problem on Arbitrary Minimal Surfaces in \({\mathbb{R}^N}\) . Results. Math. 59, 107–114 (2011). https://doi.org/10.1007/s00025-010-0064-y
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DOI: https://doi.org/10.1007/s00025-010-0064-y