Vol. 14, No. 3, 2021

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Variations of a class of Monge–Ampère-type functionals and their applications

Haodi Chen, Shibing Chen and Qi-Rui Li

Vol. 14 (2021), No. 3, 689–716

We study a class of Monge–Ampère-type functionals arising from the Lp dual Minkowski problem in convex geometry. As an application, we obtain some existence and nonuniqueness results for the problem.

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Minkowski-type problems, Monge–Ampére-type functionals, second variation, stability, nonuniqueness
Mathematical Subject Classification 2010
Primary: 35J20, 35J96
Secondary: 52A40
Received: 14 October 2018
Revised: 24 September 2019
Accepted: 2 December 2019
Published: 18 May 2021
Haodi Chen
Centre for Mathematics and Its Applications
The Australian National University
Shibing Chen
School of Mathematical Sciences
University of Science and Technology of China
Qi-Rui Li
School of Mathematical Sciences
Zhejiang University