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arXiv · 2111.05019

Uniform Poincaré inequality in o-minimal structures

Anna Valette·Guillaume Valette
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Abstract

We first define the trace on a domain $Ω$ which is definable in an o-minimal structure. We then show that every function $u\in W^{1,p}(Ω)$ vanishing on the boundary in the trace sense satisfies Poincaré inequality. We finally show, given a definable family of domains $(Ω_t)_{t\in \mathbb{R}^k}$, that the constant of this inequality remains bounded, if so does the volume of $Ω_t$.

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Anna Valette, Guillaume Valette. 2024-04-17. Uniform Poincaré inequality in o-minimal structures. https://doi.org/10.7153/mia-2023-26-11

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