A Poincaré type inequality for Hessian integrals

Research Report MRR96-067

A Poincaré type inequality for Hessian integrals

Neil S. Trudinger and Xu-Jia Wang

Abstract: In this paper we show that Hessian integrals

, $k=0, 1, \cdots, n$ , can be estimated by those of higher order. The result extends a variant of the Poincaré inequality corresponding to the cases k=0, 1. The proof depends on solving a related non-linear parabolic initial boundary value problem.

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