49 citations · 101 across the 51 of their papers we have counts for
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Principal frequencies of free non-homogeneous membranes and Sobolev extension operators
Vladimir Gol'dshtein, Valerii Pchelintsev, Alexander Ukhlov
Using the quasiconformal mappings theory and Sobolev extension operators, we obtain estimates of principal frequencies of free non-homogeneous membranes. The suggested approach is…
Composition operators on Sobolev spaces and weighted moduli inequalities
Vladimir Gol'dshtein, Evgeny Sevost'yanov, Alexander Ukhlov
In this paper we study connections between composition operators on Sobolev spaces and mappings defined by -moduli inequalities (-capacity inequalities). We prove that weight…
Singular subelliptic equations and Sobolev inequalities on nilpotent Lie groups
Prashanta Garain, Alexander Ukhlov
In this article we study singular subelliptic -Laplace equations and best constants in Sobolev inequalities on nilpotent Lie groups. We prove solvability of these subelliptic $p…
On -eigenvalues of subelliptic operators on nilpotent Lie groups
Prashanta Garain, Alexander Ukhlov
In the article we study the Dirichlet -eigenvalue problem for subelliptic non-commutative operators on nilpotent Lie groups. We prove solvability of this eigenvalue problem…
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…
Mixed local and nonlocal Sobolev inequalities with extremal and associated quasilinear singular elliptic problems
Prashanta Garain, Alexander Ukhlov
In this article, we consider mixed local and nonlocal Sobolev -inequalities with extremal in the case . We prove that the extremal of such inequalities is un…