We present upper and lower bounds for Steklov eigenvalues for domains in 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 kerne. 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.
Weyl-type bounds for Steklov eigenvalues / Provenzano, Luigi; Stubbe, Joachim. - In: JOURNAL OF SPECTRAL THEORY. - ISSN 1664-039X. - 1:9(2019), pp. 349-377. [10.4171/JST/250]
Weyl-type bounds for Steklov eigenvalues
Luigi Provenzano;
2019
Abstract
We present upper and lower bounds for Steklov eigenvalues for domains in 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 kerne. 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.File | Dimensione | Formato | |
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