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arXiv · 2111.05019

Uniform Poincar\'e inequality in o-minimal structures

Anna Valette·Guillaume Valette
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Abstract

We first define the trace on a domain $\Omega$ which is definable in an o-minimal structure. We then show that every function $u\in W^{1,p}(\Omega)$ vanishing on the boundary in the trace sense satisfies Poincar\'e inequality. We finally show, given a definable family of domains $(\Omega_t)_{t\in \mathbb{R}^k}$, that the constant of this inequality remains bounded, if so does the volume of $\Omega_t$.

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Anna Valette, Guillaume Valette. 2021-11-09. Uniform Poincar\'e inequality in o-minimal structures. https://doi.org/10.7153/mia-2023-26-11

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