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arXiv · 2411.15932

Sobolev $(p,q)$-extension operators and Neumann eigenvalues

Vladimir Gol'dshtein·Alexander Ukhlov
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Abstract

In this article, we consider $(p,q)$-extension operators, $1 < q \le p < \infty$, on Sobolev spaces. Based on composition operators on Sobolev spaces, we construct the extension operators in outward cuspidal domains with estimates of their norms. Using these $(p,q)$-extension operators, we prove estimates for the non-linear Neumann eigenvalues of the $p$-Laplace operator in outward cuspidal domains.

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Vladimir Gol'dshtein, Alexander Ukhlov. 2024-11-24. Sobolev $(p,q)$-extension operators and Neumann eigenvalues. https://arxiv.org/abs/2411.15932

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