On boundary value problems for elliptic operators in the case of domains on manifolds

摘要

In the case of the Dirichlet boundary value problem for an elliptic operator on a manifold, the smoothness of solutions is considered and the perturbations of eigenvalues under the variation of the domain are estimated. A relationship between the smoothness of the right-hand side, the regularity of the domain, and the smoothness of the solution of the problem is determined. The dependence of the perturbations of eigenvalues on the characteristics of the domain being varied and their variation are described.