49 citations · 101 across the 51 of their papers we have counts for
55 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…
The nonlinear Steklov problem in outward cuspidal domains
Pier Domenico Lamberti, Alexander Ukhlov
In this article, we consider the nonlinear Steklov eigenvalue problem in outward cuspidal domains. Using the compactness of the weighted trace embedding we obtain the variational c…
Estimates of variational eigenvalues on metric measure spaces
Prashanta Garain, Alexander Ukhlov
In the article, we study variational eigenvalues on doubling metric measure spaces. We prove existence of minimizers of variational Neumann -eigenvalues on metric measure sp…
Sobolev homeomorphisms and composition operators on homogeneous Lie groups
Alexander Ukhlov
In this article, we study Sobolev homeomorphisms and composition operators on homogeneous Lie groups. We prove that a measurable homeomorphism belongs to the S…
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…
Sobolev -extension operators and Neumann eigenvalues
Vladimir Gol'dshtein, Alexander Ukhlov
In this article, we consider -extension operators, , on Sobolev spaces. Based on composition operators on Sobolev spaces, we construct the extension op…