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

2024/12/18 by Franceschini, Federico, Savin, Ovidiu
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.13425

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 belonging to intervals of the form (2k,2k+1), k ∈ ℕ. In particular, there are no frequencies in the interval (2,3).

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