# CARMA OANT Seminar

## Monday, 10th Sep 2012

V205, Mathematics Building

# Dr Liangjin Yao

(CARMA, The University of Newcastle)

# Legendre-type integrands and convex integral functions

In this talk, we study the properties of integral functionals induced on $L_\text{E}^1(S,\mu)$ by closed convex functions on a Euclidean space E. We give sufficient conditions for such integral functions to be strongly rotund (well-posed). We show that in this generality functions such as the Boltzmann-Shannon entropy and the Fermi-Dirac entropy are strongly rotund. We also study convergence in measure and give various limiting counter-example.

This is joint work with Jon Borwein.