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

Haodi Chen; Shibing Chen; Qi-Rui Li

doi:10.2140/apde.2021.14.689

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.

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Haodi Chen. Shibing Chen. Qi-Rui Li. "Variations of a class of Monge–Ampère-type functionals and their applications." Anal. PDE 14 (3) 689 - 716, 2021. https://doi.org/10.2140/apde.2021.14.689

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Received: 14 October 2018; Revised: 24 September 2019; Accepted: 2 December 2019; Published: 2021

First available in Project Euclid: 25 June 2021

Digital Object Identifier: 10.2140/apde.2021.14.689

Subjects:

Primary: 35J20 , 35J96

Secondary: 52A40

Keywords: Minkowski-type problems , Monge–Ampére-type functionals , Nonuniqueness , second variation , stability

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