Spectral Stability Estimates of Neumann 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 Neumann boundary condition in non-Lipschitz domains $\Omega \subset \mathbb{C}$. The suggested method is based on connections of planar quasiconformal mappings with Sobolev spaces and its applications to the Poincaré inequalities.

arXiv comment15 pages. arXiv admin note: substantial text overlap with arXiv:1905.05473

References in corpus (4)

• Sharp spectral stability estimates via the Lebesgue measure of domains for higher order elliptic operators
• Conformal spectral stability for the Dirichlet-Laplace operator
• On the sharpness of a certain spectral stability estimate for the Dirichlet Laplacian
• Spectral Stability Estimates of Dirichlet Divergence Form Elliptic Operators