scholarly journals The classical Neumann problem for a class of mixed Hessian equations

2021 ◽  
Author(s):  
Chuanqiang Chen ◽  
Li Chen ◽  
Xinqun Mei ◽  
Ni Xiang
Keyword(s):  
Neumann Problem ◽  
Hessian Equations

scholarly journals Classical Neumann Problems for Hessian Equations and Alexandrov–Fenchel’s Inequalities

2018 ◽  
Vol 2019 (20) ◽  
pp. 6285-6303 ◽  
Author(s):  
Guohuan Qiu ◽  
Chao Xia
Keyword(s):  
Neumann Problem ◽  
Convex Geometry ◽  
Uniformly Convex ◽  
Convex Domains ◽  
Neumann Problems ◽  
Geometric Application ◽  
Hessian Equations

Abstract Recently, the 1st named author together, with Xinan Ma [12], has 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 for uniformly convex domains in $\mathbb {R}^{n}$. 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 by Reilly [18].

Sign in / Sign up

Export Citation Format

Share Document