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arXiv · 2607.06415

Stability for the Affine Sobolev Inequality and its Critical Points for $p\ge 2$

Rupert L. Frank·Yinqin Li·Dachun Yang
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Abstract

We prove stability for the affine Sobolev inequality for exponents $p\geq 2$ with best possible norm and best possible stability exponent. We also show a corresponding result for critical points of the functional in the absence of bubbling. An important ingredient in our proof is the classification of positive energy solutions to the critical affine $p$-Laplace equation.

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Rupert L. Frank, Yinqin Li, Dachun Yang. 2026-07-07. Stability for the Affine Sobolev Inequality and its Critical Points for $p\ge 2$. https://arxiv.org/abs/2607.06415

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