Variations of a class of Monge-Ampère-type functionals and their applications
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 \(\mathbb{S}^n\).
scientific article; zbMATH DE number 7365579
scientific article