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
Abstract

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.

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