# Spectral stability estimates of Dirichlet divergence form elliptic operators

@article{Goldshtein2020SpectralSE, title={Spectral stability estimates of Dirichlet divergence form elliptic operators}, author={Vladimir Gol'dshtein and V. A. Pchelintsev and A. Ukhlov}, journal={Analysis and Mathematical Physics}, year={2020}, volume={10}, pages={1-25} }

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

## 4 Citations

### Spectral Stability Estimates of Neumann Divergence Form Elliptic Operators

- Mathematics
- 2020

We study spectral stability estimates of elliptic operators in divergence form $-\textrm{div} [A(w) \nabla g(w)]$ with the Neumann boundary condition in non-Lipschitz domains $\Omega \subset \mathbb…

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

- Mathematics
- 2020

We study spectral estimates of the divergence form uniform elliptic operators $-\textrm{div}[A(z) \nabla f(z)]$ with the Dirichlet boundary condition in bounded non-Lipschitz simply connected domains…

### On growth monotonicity estimates of the principal Dirichlet-Laplacian eigenvalue

- Mathematics
- 2021

In the present paper we obtain growth monotonicity estimates of the principal Dirichlet-Laplacian eigenvalue in bounded non-Lipschitz domains. The proposed method is based on composition operators…

### Estimates for Variation of the First Dirichlet Eigenvalue of the Laplace Operator

- MathematicsJournal of Mathematical Sciences
- 2022

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