Weyl-type bounds for Steklov eigenvalues
Luigi Provenzano
EPFL, Lausanne, Switzerland, and Università degli Studi di Padova, ItalyJoachim Stubbe
EPFL, Lausanne, Switzerland
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Abstract
We present upper and lower bounds for Steklov eigenvalues for domains in with 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.
Cite this article
Luigi Provenzano, Joachim Stubbe, Weyl-type bounds for Steklov eigenvalues. J. Spectr. Theory 9 (2019), no. 1, pp. 349–377
DOI 10.4171/JST/250