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math.AP2026
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…
math.AP2026
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…