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math.AP2025
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…
math.AP2025
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…
math.AP2025
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…