Zobrazeno 1 - 10
of 52
pro vyhledávání: '"Menovschikov, A."'
We extend the definition of weak and strong convergence to sequences of Sobolev-functions whose underlying domains themselves are converging. In contrast to previous works, we do so without ever assuming any sort of reference configuration. We then d
Externí odkaz:
http://arxiv.org/abs/2411.10827
In this article, we study homeomorphisms $\varphi: \Omega \to \widetilde{\Omega}$ that generate embedding operators in Sobolev classes on metric measure spaces $X$ by the composition rule $\varphi^{\ast}(f)=f\circ\varphi$. In turn, this leads to Sobo
Externí odkaz:
http://arxiv.org/abs/2411.06435
Autor:
Menovschikov, Alexander
We provide the estimates for the constant in the weighted Poincar\'e inequality for a special class of planar domains and weights. Based on this, we prove the lower bounds for the first non-zero eigenvalue $\mu_\rho$ of the Neumann Laplacian with den
Externí odkaz:
http://arxiv.org/abs/2312.13204
In this paper we give characterizations of mappings generate embeddings of Sobolev spaces in the terms of ring capacity inequalities. In addition we prove that such mappings are Lipschitz mappings in the sub-hyperbolic type capacitory metrics.
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Externí odkaz:
http://arxiv.org/abs/2205.04856
We study injectivity for models of Nonlinear Elasticity that involve the second gradient. We assume that $\Omega\subset\mathbb{R}^n$ is a domain, $f\in W^{2,q}(\Omega,\mathbb{R}^n)$ satisfies $|J_f|^{-a}\in L^1$ and that $f$ equals a given homeomorph
Externí odkaz:
http://arxiv.org/abs/2204.05559
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 $Q$-homeomorphisms. Using the composition operators on Sobolev sp
Externí odkaz:
http://arxiv.org/abs/2110.09261
Publikováno v:
In Journal of Mathematical Analysis and Applications 1 March 2024 531(1) Part 1
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 $BMO$-quasiconformal mappings generate bounded composition ope
Externí odkaz:
http://arxiv.org/abs/2105.07256
Publikováno v:
SIAM J. Math. Anal. 53 (2021), no. 4, 4865-4907
We propose an extension of the classical variational theory of evolution equations that accounts for dynamics also in possibly non-reflexive and non-separable spaces. The pivoting point is to establish a novel variational structure, based on abstract
Externí odkaz:
http://arxiv.org/abs/2012.05518
We apply the metrical approach to Sobolev spaces, which arise in various evolution PDEs. Functions from those spaces are defined on an interval and take values in a family of Banach spaces. In this case we adapt the definition of Newtonian spaces. Fo
Externí odkaz:
http://arxiv.org/abs/2003.10657