Maximum principles and isoperimetric inequalities for some Monge–Ampère-type problems

In this note we derive a maximum principle for an appropriate functional combination of u(x)$u(\mathbf{x})$ and |∇u|²${|\mathrm{\nabla }u|}^2$, where u(x)$u(\mathbf{x})$ is a strictly convex classical solution to a general class of Monge–Ampère equations. This maximum principle is then employed to establish some isoperimetric inequalities of interest in the theory of surfaces of constant Gauss curvature in R^N+1${\mathbb{R}}^{N+1}$.     

Necessary and sufficient conditions of some strong optimal solutions to the interval linear programming

This paper considers optimal solutions of general interval linear programming problems. Necessary and sufficient conditions of (A,b)$(\mathbf{A},\mathbf{b})$-strong and (A,b,c)$(\mathbf{A},\mathbf{b},\mathbf{c})$-strong optimal solutions to the interval linear programming with inequality constraints are proposed. The features of the proposed methods are illustrated by some examples.