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arXiv · 2601.19359

A sharp monomial Caffarelli-Kohn-Nirenberg inequality

Francesco Pagliarin
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Abstract

We consider a monomial Caffarelli-Kohn-Nirenberg inequality, find the optimal constant and classify the optimizers under an integrated curvature dimension condition. We take advantage of the $\Gamma$-calculus to exploit geometrical techniques to tackle the problem and regularity results to justify some integration by parts. A symmetry-breaking result is also provided.

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Francesco Pagliarin. 2026-01-27. A sharp monomial Caffarelli-Kohn-Nirenberg inequality. https://arxiv.org/abs/2601.19359

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