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Abstract <p> We prove two-term spectral asymptotics for the Riesz means of the eigenvalues of the Laplacian on a Lipschitz domain with Robin boundary conditions. The second term is the same as in the case of Neumann boundary conditions. This is valid for Riesz means of arbitrary positive order. For orders at least one and under additional assumptions on the function determining the boundary conditions, we derive leading order asymptotics for the difference between Riesz means of Robin and Neumann eigenvalues. </p>

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Spectral Asymptotics for Robin Laplacians on Lipschitz Sets

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Simon Larson,
  • Rupert L. Frank

摘要

Abstract

We prove two-term spectral asymptotics for the Riesz means of the eigenvalues of the Laplacian on a Lipschitz domain with Robin boundary conditions. The second term is the same as in the case of Neumann boundary conditions. This is valid for Riesz means of arbitrary positive order. For orders at least one and under additional assumptions on the function determining the boundary conditions, we derive leading order asymptotics for the difference between Riesz means of Robin and Neumann eigenvalues.