4 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…
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 $Ï^{\as…
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…