Estimates of Dirichlet eigenvalues of divergent elliptic operators in non-Lipschitz domains

Abstract

We study spectral estimates of the divergence form uniform elliptic operators $-\text{div}[A(z)\nabla f(z)]$ with the Dirichlet boundary condition in bounded non-Lipschitz simply connected domains $\Omega \subset \mathbb{C}$. The suggested method is based on the quasiconformal composition operators on Sobolev spaces with applications to the weighted Poincaré-Sobolev inequalities.

13 pages

References in corpus (1)

• Spectral Stability Estimates of Dirichlet Divergence Form Elliptic Operators