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arXiv · 2609.28152

Discrete Sobolev and Trudinger inequalities on polyhedral meshes

Maxime Herda·Ariane Trescases·Antoine Zurek
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Abstract

We revisit the derivation of discrete Sobolev and related inequalities on bounded domains for piecewise constant functions on polyhedral meshes. Our results improve the dependence of the Sobolev constant on the Lebesgue exponents and allow us to recover the asymptotics of the continuous case. As a consequence we derive a discrete version of the Trudinger inequality and variants. We extend our results to broken Sobolev spaces and discuss implications of these new or refined discrete functional inequalities in the numerical analysis of non-conforming numerical methods.

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Maxime Herda, Ariane Trescases, Antoine Zurek. 2026-09-23. Discrete Sobolev and Trudinger inequalities on polyhedral meshes. https://arxiv.org/abs/2609.28152

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