English

Sharp Weyl-Type Formulas of the Spectral Functions for Biharmonic Steklov Eigenvalues

Analysis of PDEs 2012-04-03 v2

Abstract

In this paper, by explicitly calculating the principal symbols of pseudodifferential operators and by applying H\"omander's spectral function theorem, we obtain the Weyl-type asymptotic formulas with sharp remainder estimates for the counting functions of the two classes of biharmonic Steklov eigenvalues λk\lambda_k and μk\mu_k in a smooth bounded domain of a Riemannian manifold. This solves a longstanding challenging problem.

Keywords

Cite

@article{arxiv.1112.1206,
  title  = {Sharp Weyl-Type Formulas of the Spectral Functions for Biharmonic Steklov Eigenvalues},
  author = {Genqian Liu},
  journal= {arXiv preprint arXiv:1112.1206},
  year   = {2012}
}

Comments

24 pages. arXiv admin note: substantial text overlap with arXiv:1105.0076

R2 v1 2026-06-21T19:46:59.428Z