SMS scnews item created by Daniel Hauer at Tue 13 Aug 2019 1802
Type: Seminar
Distribution: World
Expiry: 19 Aug 2019
Calendar1: 19 Aug 2019 1200-1300
CalLoc1: AGR Carslaw 829
CalTitle1: On the Hermite-Hadamard formula in higher dimensions
Auth: dhauer@120.17.61.185 (dhauer) in SMS-WASM

PDE Seminar

On the Hermite-Hadamard formula in higher dimensions

Barbara Brandolini

Università degli Studi di Napoli “Federico II”, Italy

Mon 19th Aug 2019, 12-1pm, Carslaw Room 829 (AGR)

Abstract

Let Ω n be a convex domain and let f : Ω be a positive, subharmonic function (i.e. Δf 0). Then

1 |Ω|Ωfdx cn |Ω|Ωfdσ,

where cn 2n32. This inequality was previously only known for convex functions with a much larger constant. We also show that the optimal constant satisfies cn n - 1. As a byproduct, we establish the following sharp geometric inequality for two convex domains where one contains the other Ω2 Ω1 n:

|Ω1| |Ω1| |Ω2| |Ω2| n.


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