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arXiv · 2605.00795

Compactness of weighted Sobolev trace operators and non-linear Steklov problems

Alexander Menovschikov·Alexander Ukhlov
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Abstract

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 non-linear Steklov problem in outward cuspidal domains in a correct functional setting and to establish the existence of its non-trivial solution.

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Alexander Menovschikov, Alexander Ukhlov. 2026-05-01. Compactness of weighted Sobolev trace operators and non-linear Steklov problems. https://arxiv.org/abs/2605.00795

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