Spectral Stability Estimates of Dirichlet Divergence Form Elliptic Operators

Abstract

We study spectral stability estimates of elliptic operators in divergence form $-\text{div}[A(w)\nabla g(w)]$ with the Dirichlet boundary condition in non-Lipschitz domains $\tilde{\Omega }\subset \mathbb{C}$. The suggested method is based on connections of planar quasiconformal mappings with Sobolev spaces and its applications to the Poincaré inequalities.

18 pages. arXiv admin note: text overlap with arXiv:1903.11301

References in corpus (1)

• On the sharpness of a certain spectral stability estimate for the Dirichlet Laplacian

Cited by in corpus (2)

• Spectral Stability Estimates of Neumann Divergence Form Elliptic Operators
• Estimates of Dirichlet eigenvalues of divergent elliptic operators in non-Lipschitz domains