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

@article{Goldshtein2017IntegralEO, title={Integral estimates of conformal derivatives and spectral properties of the Neumann-Laplacian}, author={Vladimir Gol'dshtein and V. A. Pchelintsev and Alexander Ukhlov}, journal={Journal of Mathematical Analysis and Applications}, year={2017} }

## 19 Citations

### On conformal spectral gap estimates of the Dirichlet–Laplacian

- Mathematics
- 2018

We study spectral stability estimates of the Dirichlet eigenvalues of the Laplacian in non-convex domains $\Omega\subset\mathbb R^2$. With the help of these estimates we obtain asymptotically sharp…

### 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…

### 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…

### On the First Eigenvalue of the Degenerate $p$-Laplace Operator in Non-Convex Domains

- Mathematics
- 2017

In this paper we obtain lower estimates of the first non-trivial eigenvalues of the degenerate $p$-Laplace operator, $p>2$, in a large class of non-convex domains. This study is based on applications…

### 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…

### On the First Eigenvalue of the Degenerate $$\varvec{p}$$p-Laplace Operator in Non-convex Domains

- MathematicsIntegral Equations and Operator Theory
- 2018

In this paper we obtain lower estimates of the first non-trivial eigenvalues of the degenerate p-Laplace operator, $$p>2$$p>2, in a large class of non-convex domains. This study is based on…

### On Variations of the Neumann Eigenvalues of p-Laplacian Generated by Measure Preserving Quasiconformal Mappings

- MathematicsJournal of Mathematical Sciences
- 2021

We study variations of the first nontrivial eigenvalue of the two-dimensional p-Laplace operator, p > 2, generated by measure preserving quasiconformal mappings. The study is based on the geometric…

### Space quasiconformal composition operators with applications to Neumann eigenvalues

- Mathematics
- 2020

In this article we obtain estimates of Neumann eigenvalues of p -Laplace operators in a large class of space domains satisfying quasihyperbolic boundary conditions. The suggested method is based on…

### Sobolev extension operators and Neumann eigenvalues

- MathematicsJournal of Spectral Theory
- 2020

In this paper we apply estimates of the norms of Sobolev extension operators to the spectral estimates of of the first nontrivial Neumann eigenvalue of the Laplace operator in non-convex extension…

### On the principal frequency of non-homogeneous membranes

- Mathematics
- 2023

. We obtained estimates for ﬁrst eigenvalues of the Dirichlet boundary value problem for elliptic operators in divergence form (i.e. for the principal frequency of non-homogeneous membranes) in…

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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…

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We prove a Payne-Weinberger type inequality for the $p$-Laplacian Neumann eigenvalues ($p\ge 2$). The inequality provides the sharp upper bound on convex domains, in terms of the diameter alone, of…

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The authors consider bounds on the Neumann eigenvalues of the Laplacian on domains in $I\mathbb{R}^n $ in the light of their recent results on Dirichlet eigenvalues, in particular, their proof of t...