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

@inproceedings{Pchelintsev2021OnGM, title={On growth monotonicity estimates of the principal Dirichlet-Laplacian eigenvalue}, author={V. A. Pchelintsev}, year={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 generated by quasiconformal mappings and their applications to weighted Sobolev inequalities.

## References

SHOWING 1-10 OF 31 REFERENCES

Spectral properties of the Neumann-Laplace
operator in quasiconformal regular domains

- MathematicsContemporary Mathematics
- 2019

In this paper we study spectral properties of the Neumann-Laplace operator in planar quasiconformal regular domains $\Omega\subset\mathbb R^2$. This study is based on the quasiconformal theory of…

Spectral stability estimates of Dirichlet divergence form elliptic operators

- MathematicsAnalysis and Mathematical Physics
- 2020

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…

Extremum Problems for Eigenvalues of Elliptic Operators

- Mathematics
- 2006

Eigenvalues of elliptic operators.- Tools.- The first eigenvalue of the Laplacian-Dirichlet.- The second eigenvalue of the Laplacian-Dirichlet.- The other Dirichlet eigenvalues.- Functions of…

Integral estimates of conformal derivatives and spectral properties of the Neumann-Laplacian

- MathematicsJournal of Mathematical Analysis and Applications
- 2018

Weighted Sobolev spaces and embedding theorems

- Mathematics
- 2007

In the present paper we study embedding operators for weighted Sobolev spaces whose weights satisfy the well-known Muckenhoupt A p -condition. Sufficient conditions for boundedness and compactness of…

On the First Eigenvalues of Free Vibrating Membranes in Conformal Regular Domains

- Mathematics
- 2016

AbstractIn 1961 G. Polya published a paper about the eigenvalues of vibrating membranes. The “free vibrating membrane” corresponds to the Neumann–Laplace operator in bounded plane domains. In this…

Quasihyperbolic boundary conditions and capacity: Hölder continuity of quasiconformal mappings

- Mathematics
- 2001

Abstract. We prove that quasiconformal maps onto domains which satisfy a quasihyperbolic boundary condition are globally Hölder continuous in the internal metric. The primary improvement here over…

Applications of change of variables operators for exact embedding theorems

- Mathematics
- 1994

We propose here a new method for the investigation of embedding operators. It is based on an exact description of classes of homeomorphisms that induce change of variables operators on the Sobolev…

Quasihyperbolic boundary conditions and Poincaré domains

- Mathematics
- 2002

Abstract. We prove that a domain in
${\Bbb R}^n$ whose quasihyperbolic metric satisfies a logarithmic growth condition with coefficient
$\beta\le 1$ is a (q,p)-\Poincare domain for all p and q…