Dilatation and the asymptotics of the eigenvalues of spectral problems with singularities
The eigenvalue problem \(Au=\lambda^ 2\mu u\) is investigated providing that A is a uniformly elliptic selfadjoint operator of the 2nd order and \(\mu\) is a nonnegative weight function. The term singularity means either the nonregularity of \(\mu\) or of the coefficients of A, degeneration of \(\mu\), unboundedness of the domain or nonregularity of the boundary. It is shown how the method of dilatations facilitates to derive very precise asymptotics of eigenvalues of the spectral problem with sufficiently weak singularities.
scientific article; zbMATH DE number 4021768
scientific article