Weighted Sobolev spaces and embedding theorems
- V. Gol'dshtein, A. Ukhlov
- Mathematics
- 24 March 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…
Sobolev spaces and (P,Q)-quasiconformal mappings of carnot groups
- S. K. Vodop’yanov, A. Ukhlov
- Mathematics
- 1 August 1998
Approximately differentiable transformations and change of variables on nilpotent groups
- S. K. Vodop’yanov, A. Ukhlov
- Mathematics
- 1996
Sobolev spaces and mappings with bounded (P,Q)-distortion on Carnot groups
- A. Ukhlov, S. Vodopyanov
- Mathematics
- 4 September 2007
Embeddings of weighted Sobolev spaces and degenerate Dirichlet problems involving the weighted p-Laplacian
- V. Gol'dshtein, V. V. Motreanu, A. Ukhlov
- Mathematics
- 15 September 2011
We deal with two Dirichlet boundary value problems involving the weighted p-Laplacian. We introduce double weighted Sobolev spaces as solution spaces of the considered problems. We show the existence…
Quasiconformal mappings and Neumann eigenvalues of divergent elliptic operators
- V. Gol'dshtein, V. Pchelintsev, A. Ukhlov
- MathematicsComplex Variables and Elliptic Equations
- 27 March 2019
We study spectral properties of divergence form elliptic operators with the Neumann boundary condition in planar domains (including some fractal type domains) that satisfy to the quasihyperbolic…
Extension operators on Sobolev spaces with decreasing integrability.
- A. Ukhlov
- Mathematics
- 25 August 2019
We study extension operators on Sobolev spaces with decreasing integrability on the base of set functions associated with the operator norms. Sharp necessary conditions in the terms of the weak…
On the First Eigenvalues of Free Vibrating Membranes in Conformal Regular Domains
- V. Gol'dshtein, A. Ukhlov
- Mathematics
- 21 May 2015
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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