Balogh, Z.M., Don, S. & Kristály, A. (2024) Transactions of the American Mathematical Society [Matematică, Q1]

Publicat: 14 Iunie 2024

Balogh, Z.M., Don, S. & Kristály, A. (2024) Sharp weighted log-Sobolev inequalities: Characterization of equality cases and applications. Transactions of the American Mathematical Society, 377, 5129-5163.

DOI: https://doi.org/10.1090/tran/9163

✓ Publisher: American Mathematical Society
✓ Categories: Mathematics
✓ Article Influence Score (AIS): 1.401 (2023) / Q1

Abstract: By using optimal mass transport theory, we provide a direct proof to the sharp L-p-log-Sobolev inequality (p >= 1) involving a log -concave homogeneous weight on an open convex cone E subset of R-n. The perk of this proof is that it allows to characterize the extremal functions realizing the equality cases in the L-p-log-Sobolev inequality. The characterization of the equality cases is new for p > n even in the unweighted setting and E = R-n. As an application, we provide a sharp weighted hypercontractivity estimate for the Hopf-Lax semigroup related to the Hamilton-Jacobi equation, characterizing also the equality cases.

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