English

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

Analysis of PDEs 2024-12-19 v1

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 λ\lambda belonging to intervals of the form (2k,2k+1)(2k,2k+1), kNk \in \mathbb{N}. In particular, there are no frequencies in the interval (2,3)(2,3).

Cite

@article{arxiv.2412.13425,
  title  = {A note on the frequency gaps between integers in the thin obstacle problem},
  author = {Federico Franceschini and Ovidiu Savin},
  journal= {arXiv preprint arXiv:2412.13425},
  year   = {2024}
}
R2 v1 2026-06-28T20:39:44.313Z