#### 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 ${L}_{p}$ 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