Asymptotic distribution of eigenvalues for elliptic boundary value problems

Abstract

We consider the Weyl formula describing the asymptotic behaviour of the number of eigenvalues $N(\lambda)$ for elliptic boundary value problems. The remainder estimate of the form $N(\lambda){\rm O}(\lambda^{-\mu})$ is proved with $\mu<r/(2m)$ in the case of operators of order $2m$ with Hölder coefficients of exponent $r\in \,]0; 1]$ .