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arXiv · 2605.03668

Quantitative stability for the Trudinger-Moser inequality

João Henrique Andrade·José Francisco de Oliveira·João Marcos do Ò·Abiel Costa Macedo·Jesse Ratzkin
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Abstract

We establich quantitative stability estimates for the Trudinger-Moser inequality on smooth, bounded domains in the Euclidean plane. More specifically, we prove that the deficit in the Trudinger-Moser inequality quadratically controls the distance to the set of optimizers if either (i) the exponential rate of growth is sufficiently small or (ii) the domain is a round disk. The latter estimate remains valid even in the critical case. Both proofs rely on a new spectral gap that we prove, which may be of independent interest. Additionally we show that the same stability estimate holds in the nondegenerate case, and that this occurs generically.

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João Henrique Andrade, José Francisco de Oliveira, João Marcos do Ò, Abiel Costa Macedo, Jesse Ratzkin. 2026-05-05. Quantitative stability for the Trudinger-Moser inequality. https://arxiv.org/abs/2605.03668

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