Spectral stability under \(L^ p\)-perturbation of the second-order coefficients
Spectral stability is studied for a second order uniformly elliptic operator with real measurable coefficients, satisfying Dirichlet boundary conditions. First, stability estimates for the eigenvalues are proved for the operators with \(L^p\) coefficients. In the main theorem the author establishes the Lipschitz continuity of the resolvent in trace ideals. Such a result not only implies eigenvalue stability, it also yields stability of the spectral projections and, hence, of eigenvalues and eigenfunctions. In the last part of the paper the results are applied to the problem of heat transport affected by small impurities.
scientific article; zbMATH DE number 842907