Compactness of weighted Sobolev trace operators and non-linear Steklov problems
Analysis of PDEs
2026-05-04 v1
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.
Cite
@article{arxiv.2605.00795,
title = {Compactness of weighted Sobolev trace operators and non-linear Steklov problems},
author = {Alexander Menovschikov and Alexander Ukhlov},
journal= {arXiv preprint arXiv:2605.00795},
year = {2026}
}
Comments
19 pages