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

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.

Disclosure

“p dµ(x) < ∞, then (D.2) implies (D.1). Otherwise, one easily verifies that (D.1) R holds trivially. This completes the proof of the present lemma. □ Acknowledgements The authors acknowledge the use of AI tools during the exploratory stage of this project. All mathematical arguments and proofs in the final manuscript were checked and written by the authors. References [1] C. O. Alves, Existence of positive solutions for a problem with lack of”

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2026-08-24T00:34:12.480Z

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