Asymptotic behavior of spectral functions for elliptic operators with non-smooth coefficients

摘要

We consider the asymptotic formula of spectral functions for elliptic operators with nonsmooth coefficients of order 2m in R-n. If the coefficients of top order are Holder continuous of exponent tau epsilon (0, 1], we can derive the remainder estimate of the form 0(t((n-0)/2m)) with any thetaepsilon(0, tau). This result holds without the condition 2m>n, which was always assumed in many papers. We also show that the spectral function is differentiable up to order