Details

Autor(en) / Beteiligte

• Provenzano, Luigi
• Stubbe, Joachim

Titel

Weyl-type bounds for Steklov eigenvalues

Ist Teil von

• Journal of spectral theory, 2019-01, Vol.9 (1), p.349-377

Ort / Verlag

Zuerich, Switzerland: European Mathematical Society Publishing House

Erscheinungsjahr

2019

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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.