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research article
Weyl-type bounds for Steklov eigenvalues
January 1, 2019
We present upper and lower bounds for Steklov eigenvalues for domains in RN+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.
Type
research article
Web of Science ID
WOS:000455439300012
Authors
Publication date
2019-01-01
Publisher
Published in
Volume
9
Issue
1
Start page
349
End page
377
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
January 25, 2019
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