## 16 Citations

### Composition Operators on Sobolev Spaces and Neumann Eigenvalues

- MathematicsComplex Analysis and Operator Theory
- 2018

In this paper we discuss applications of the geometric theory of composition operators on Sobolev spaces to the spectral theory of non-linear elliptic operators. Lower estimates of the first…

### 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…

### 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…

### Space Quasiconformal Mappings and Neumann Eigenvalues in Fractal Domains

- Mathematics
- 2017

We study the variation of the Neumann eigenvalues of the $p$-Laplace operator under quasiconformal perturbations of space domains. This study allows to obtain lower estimates of the Neumann…

### Space quasiconformal mappings and Neumann eigenvalues in fractal type domains

- MathematicsGeorgian Mathematical Journal
- 2018

Abstract We study the variation of Neumann eigenvalues of the p-Laplace operator under quasiconformal perturbations of space domains. This study allows us to obtain the lower estimates of Neumann…

### Composition operators on Hardy-Sobolev spaces and BMO-quasiconformal mappings

- MathematicsUkrainian Mathematical Bulletin
- 2021

In this paper, we consider composition operators on Hardy-Sobolev spaces in connections with $\BMO$-quasiconformal mappings. Using the duality of Hardy spaces and $\BMO$-spaces, we prove that…

### Composition operators on Sobolev spaces, $Q$-mappings and weighted Sobolev inequalities

- Mathematics
- 2021

. In this paper we give connections between mappings which generate bounded composition operators on Sobolev spaces and Q -mappings. On this base we obtain measure distortion properties Q…

### Sobolev Mappings and Moduli Inequalities on Carnot Groups

- MathematicsJournal of Mathematical Sciences
- 2020

We study the mappings that satisfy moduli inequalities on Carnot groups. We prove that the homeomorphisms satisfying the moduli inequalities ($Q$-homeomor\-phisms) with a locally integrable function…

### 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…

### On regularity of weighted Sobolev homeomorphisms

- Mathematics
- 2022

. We study the weak regularity of mappings inverse to weighted Sobolev homeomorphisms ϕ : Ω → e Ω , where Ω and e Ω are domains in R n . Using the weak regularity of inverse mappings we obtain the…

## References

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### Conformal spectral stability for the Dirichlet-Laplace operator

- Mathematics
- 2014

We study the eigenvalue problem for the Dirichlet Laplacian in bounded simply connected plane domains $\Omega\subset\mathbb{C}$ using conformal transformations of the original problem to the weighted…

### Conformal spectral stability estimates for the Dirichlet Laplacian

- Mathematics
- 2015

We study the eigenvalue problem for the Dirichlet Laplacian in bounded simply connected plane domains Ω⊂C by reducing it, using conformal transformations, to the weighted eigenvalue problem for the…

### 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…

### About homeomorphisms that induce composition operators on Sobolev spaces

- Mathematics
- 2010

We study generalizations of the quasiconformal homeomorphisms (the so-called homeomorphisms with bounded (p, q)-distortion) that induce bounded composition operators on the Sobolev spaces with the…

### Conformal Weights and Sobolev Embeddings

- Mathematics
- 2013

We study embeddings of the Sobolev space $$ {\mathop{W}\limits_{~}^{\circ}}{{~}_2^1}\left( \Omega \right) $$ into weighted Lebesgue spaces Lq(Ω, h) with the so-called universal conformal weight h…

### Homeomorphisms that induce monomorphisms of Sobolev spaces

- Mathematics
- 1995

LetG, G′ be domains in ℝn. We obtain a geometrical description of the class of all homeomorphisms ϕ:G→ G′ that induce bounded operators ϕ* from the seminormed Sobolev spaceLp1(G′) toLp1(G) by the…

### Sharp Estimates for Eigenfunctions of a Neumann Problem

- Mathematics
- 2009

In this paper we provide some bounds for eigenfunctions of the Laplacian with homogeneous Neumann boundary conditions in a bounded domain Ω of ℝ n . To this aim we use the so-called symmetrization…

### Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems

- MathematicsProceedings of the Royal Society of Edinburgh: Section A Mathematics
- 2015

In this paper we prove a sharp lower bound for the first non-trivial Neumann eigenvalue μ1(Ω) for the p-Laplace operator (p > 1) in a Lipschitz bounded domain Ω in ℝn. Our estimate does not require…