Weyl-type bounds for Steklov eigenvalues

Luigi Provenzano; Joachim Stubbe

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arXiv · 1611.00929

Weyl-type bounds for Steklov eigenvalues

Luigi Provenzano·Joachim Stubbe

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Abstract

We present upper and lower bounds for Steklov eigenvalues for domains in $\mathbb{R}^{N+1}$ with $C^2$ boundary compatible with the Weyl asymptotics. In particular, we obtain sharp upper bounds on Riesz-means and the trace of corresponding Steklov heat kernel. The key result is a comparison of Steklov eigenvalues and Laplacian eigenvalues on the boundary of the domain by applying Pohozaev-type identities on an appropriate tubular neigborhood of the boundary and the min-max principle. Asymptotically sharp bounds then follow from bounds for Riesz-means of Laplacian eigenvalues.

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BibTeX RIS

Luigi Provenzano, Joachim Stubbe. 2016-11-03. Weyl-type bounds for Steklov eigenvalues. https://arxiv.org/abs/1611.00929

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