Weyl-type bounds for Steklov eigenvalues

  • Luigi Provenzano

    EPFL, Lausanne, Switzerland, and Università degli Studi di Padova, Italy
  • Joachim Stubbe

    EPFL, Lausanne, Switzerland
Weyl-type bounds for Steklov eigenvalues cover

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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