A note on the frequency gaps between integers in the thin obstacle problem

Federico Franceschini; Ovidiu Savin

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arXiv · 2412.13425

A note on the frequency gaps between integers in the thin obstacle problem

Federico Franceschini·Ovidiu Savin

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Abstract

We give a simple proof of the fact that - in all dimensions - there are no homogeneous solutions to the thin obstacle problem with frequency $\lambda$ belonging to intervals of the form $(2k,2k+1)$, $k \in \mathbb{N}$. In particular, there are no frequencies in the interval $(2,3)$.

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Federico Franceschini, Ovidiu Savin. 2024-12-18. A note on the frequency gaps between integers in the thin obstacle problem. https://arxiv.org/abs/2412.13425

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