Classical Neumann Problems for Hessian equations and Alexandrov-Fenchel's inequalities

2016/07/13 by Qiu, Guohuan, Xia, Chao · 1 citation
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1607.03868

Abstract

Recently, the first named author together with Xinan Ma \citema2015neumann, have proved the existence of the Neumann problems for Hessian equations. In this paper, we proceed further to study classical Neumann problems for Hessian equations. We prove here the existence of classical Neumann problems under the uniformly convex domain in Rⁿ. As an application, we use the solution of the classical Neumann problem to give a new proof of a family of Alexandrov-Fenchel inequalities arising from convex geometry. This geometric application is motivated from Reilly \citeReilly1980.

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• General monotone formula for homogeneous k-Hessian equation in the exterior domain and its applications

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