Weyl-type bounds for Steklov eigenvalues
Luigi Provenzano, Joachim Stubbe · Journal of Spectral Theory · 2018
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.