8 citations · 18 across the 10 of their papers we have counts for
11 papers
Compactness of weighted Sobolev trace operators and non-linear Steklov problems
Alexander Menovschikov, Alexander Ukhlov
We prove the compactness of weighted Sobolev trace operators in outward cuspidal domains by using composition operators on Sobolev spaces. This result allows us to formulate the no…
Nonlinear Neumann eigenvalues in outward cuspidal domains with weighted measure
Alexander Menovschikov, Alexander Ukhlov
We consider the nonlinear Neumann eigenvalue problem in outward cuspidal domains with a weighted measure. Using composition operators on Sobolev spaces, we establish embeddings of…
Zero-extension convergence and Sobolev spaces on changing domains
Nikita Evseev, Malte Kampschulte, Alexander Menovschikov
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 s…
On mappings generating embedding operators in Sobolev classes on metric measure spaces
Alexander Menovschikov, Alexander Ukhlov
In this article, we study homeomorphisms that generate embedding operators in Sobolev classes on metric measure spaces by the composition rule $φ^{\ast}(f…
Capacity of rings and mappings generate embeddings of Sobolev spaces
Alexander Menovschikov, Alexander Ukhlov
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 Li…
Composition operators on Sobolev spaces, -mappings and weighted Sobolev inequalities
Alexander Menovschikov, Alexander Ukhlov
In this paper we give connections between mappings which generate bounded composition operators on Sobolev spaces and -mappings. On this base we obtain measure distortion proper…
Composition operators on Hardy-Sobolev spaces and -quasiconformal mappings
Alexander Menovschikov, Alexander Ukhlov
In this paper we consider composition operators on Hardy-Sobolev spaces in connections with -quasiconformal mappings. Using the duality of Hardy spaces and -spaces we pro…
An extended variational theory for nonlinear evolution equations via modular spaces
Alexander Menovschikov, Anastasia Molchanova, Luca Scarpa
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…
Sobolev space of functions valued in a monotone Banach family
Nikita Evseev, Alexander Menovschikov
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 Banac…
Decomposable operators acting between distinct -direct integrals of Banach spaces
Nikita Evseev, Alexander Menovschikov
The notion of decomposable operators acting between distinct -direct integrals of Banach spaces is introduced. We show that these operators generalize the composition operator…
Bounded operators on mixed norm Lebesgue spaces
Nikita Evseev, Alexander Menovschikov
We study two classes of bounded operators on mixed norm Lebesgue spaces, namely composition operators and product operators. A complete description of bounded composition operators…