Spectral boundary value problems for Laplace--Beltrami operator: moduli of continuity of eigenvalues under domain deformation

摘要

The paper is pertaining to the spectral theory of operators and boundaryvalue problems for differential equations on manifolds. Eigenvalues of suchproblems are studied as functionals on the space of domains. Resolventcontinuity of the corresponding operators is established under domaindeformation and estimates of continuity moduli of their eigenvalues $\slash$eigenfunctions are obtained provided the boundary of nonperturbed domain islocally represented as a graph of some continuous function and domaindeformation is measured with respect to the Hausdorff--Pompeiu metric.