For every bounded Lipschitz domain, Pólya's eigenvalue bound holds up to factor 1+ε for all eigenvalues above an explicit threshold, and exact Pólya bounds are proved for new irregular domain classes.
and Lieb E.H., On semiclassical bounds for eigenvalues of Schr ¨odinger op- erators,Phys
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P\'olya's conjecture up to $\epsilon$-loss and quantitative estimates for the remainder of Weyl's law
For every bounded Lipschitz domain, Pólya's eigenvalue bound holds up to factor 1+ε for all eigenvalues above an explicit threshold, and exact Pólya bounds are proved for new irregular domain classes.