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A Poincaré type inequality for Hessian integrals

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Abstract.

In this paper we show that Hessian integrals \(I_k\), \(k=0, 1, \cdots, n\), 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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Authors and Affiliations

  1. Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, Australia (e-mail: Neil.Trudinger@maths.anu.edu.au, X.J.Wang@maths.anu.edu.au) , , , , , , AU

    Neil S. Trudinger & Xu-Jia Wang

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  1. Neil S. Trudinger
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  2. Xu-Jia Wang
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Received January 15, 1997 / Accepted March 1997

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Trudinger, N., Wang, XJ. A Poincaré type inequality for Hessian integrals. Calc Var 6, 315–328 (1998). https://doi.org/10.1007/s005260050093

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  • DOI: https://doi.org/10.1007/s005260050093

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