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 and in a smooth bounded domain of a Riemannian manifold. This solves a longstanding challenging problem.
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