Variations of a class of Monge-Ampère-type functionals and their applications
type: Item
instance of: scholarly article
title: Variations of a class of Monge-Ampère-type functionals and their applications
zbMATH Open document ID: 1468.35047
author: Haodi Chen
author: Shibing Chen
author: Qi-Rui Li
published in: Analysis \& PDE
publication date: 2021-07-01T00:00:00Z
review text: This article investigates a class of Monge-Ampere functionals arising from the \(L^p\) dual Minkowski problem in convex geometry. As an application, the authors obtain some existence and nonuniqueness results for the problem \(\mathrm{det}(\nabla^2u+u)=(u^2+|\nabla u|^2)^{(n+1-q)/2}f(x)\) in \(\mathbb{S}^n\), where \(\nabla ^2u\) denotes the covariant derivative with respect to an orthonormal frame on \(\mathbb{S}^n\).
reviewed by: Marius Ghergu
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35J96
Mathematics Subject Classification ID: 52A40
zbMATH DE Number: 7365579
zbMATH Keywords: Minkowski-type problems
zbMATH Keywords: Monge-Ampère-type functionals
zbMATH Keywords: second variation
zbMATH Keywords: stability
zbMATH Keywords: nonuniqueness
MaRDI profile type: Publication
full work available at URL: apde.2021.14.689
OpenAlex ID: W3160059718
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DOI: 10.2140/APDE.2021.14.689
description: scientific article; zbMATH DE number 7365579