Balogh, Z.M., Don, S. & Kristály, A. (2025) SIAM Journal on Applied Mathematics [Matematică, Q1]

Publicat: 10 Mai 2025

Balogh, Z.M., Don, S. & Kristály, A. (2025), Weighted Gagliardo–Nirenberg Inequalities via Optimal Transport Theory and Applications. SIAM Journal on Applied Mathematics , 57(3), 2175–2209.

DOI: https://doi.org/10.1137/24M1649575

✓ Publisher: SIAM
✓ Categories: Mathematics, Applied
✓ Article Influence Score (AIS): 0.988 (2023) / Q1

Abstract: We prove Gagliardo–Nirenberg inequalities with three weights—verifying a joint concavity condition—on open convex cones of Rn. If the weights are equal to each other the inequalities become sharp and we compute explicitly the sharp constants. For a certain range of parameters we can characterize the class of extremal functions; in this case, we also show that the sharpness in the main three-weighted Gagliardo–Nirenberg inequality implies that the weights must be equal up to some constant multiplicative factors. Our approach uses optimal mass transport theory and a careful analysis of the joint concavity condition of the weights. As applications we establish sharp weighted p-log-Sobolev, Faber–Krahn, and isoperimetric inequalities with explicit sharp constants.

inapoi la stiri   vezi evenimentele   home