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Seventh Mississippi State - UAB Conference on Differential Equations & Computational Simulations
November 1-3, 2007
Doubletree Hotel
Birmingham, AL, USA

Organizers
Mississippi State University & University of Alabama - Birmingham

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Brunn-Minkowski type Inequalities related to the Monge-Ampère Equation
by
David Hartenstine
Western Washington University

Let W ⊂ Rn be strictly convex and let 0 ≤ p < n. Define the functional Fp(W) = -∫W u det D2 u, where u solves the homogeneous Dirichlet problem for the Monge-Ampère equation det D2 u = |u|p in W. Generalizing results known for the Laplace and p-Laplace operators, Fp satisfies a Brunn-Minkowski type inequality. In the case p=0, equality conditions for this inequality will also be established. Related open problems will also be presented.

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Date received: August 31, 2007

Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cauf-82.