Asymptotic distribution of eigenvalues for some elliptic operators with intermediate remainder estimate
Lech Zieliński · Asymptotic Analysis · 1998
We consider the Weyl formula for the asymptotic number of eigenvalues $N(\lambda)$ for some elliptic operators. We prove remainder estimates of the form $N(\lambda){\rm O}(\lambda^{-\mu})$ with $\mu$ depending on the regularity of coefficients and ranging between 0 and the optimal value in the standard situation of smooth coefficients, i.e., $0<\mu<2/m$ in the case of globally elliptic operators on ${\NBbbR}^d$ , and $0<\mu<1/m$ in the case of a smooth compact manifold without boundary, where $m$ is the degree of the considered operators.