Continuity aspects for traces of Dirichlet forms with respect to monotone weak convergence of G-Kato measures
Abstract
We investigate some analytic properties of traces of Dirichlet forms with respect to measures satisfying Hardy-type inequality. Among other results, we prove convergence of spectra, ordered eigenvalues, and eigenfunctions, as well as convergence of resolvents on appropriate spaces, for traces of Dirichlet forms when the speed measure is the monotone weak limit of G-Kato measures. Some quantitative estimates are also given. As applications, we show continuity of stationary solutions of some elliptic operators with measure-valued coefficients with respect to the coefficients and give an approximation procedure for the eigenvalues of a one-dimensional graph Laplacian as well as for the Laplacian on annular thin sets with mixed Neumann–Wentzell boundary conditions.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
advanced mathematical theories
Advanced Algebra and Geometry
Publication details
- Journal / source
- Kyoto journal of mathematics
- Publisher
- Duke University Press
- Volume
- 66
- Issue
- 3
- Pages
- 691-717
- Publication date
- 2 June 2026
- Language
- EN