SOME MAXIMUM PRINCIPLES AND SYMMETRY RESULTS FOR A CLASS OF BOUNDARY VALUE PROBLEMS INVOLVING THE MONGE-AMPÈRE EQUATION
2001 ◽
Vol 11
(06)
◽
pp. 1073-1080
◽
Keyword(s):
In this paper we investigate a class of boundary value problems for the Monge-Ampère equation [Formula: see text] where Ω is a strictly convex bounded domain in RN, N≥2. When f=g(u)h(|∇u|2) with g and h satisfying the differential inequality [Formula: see text] we show in Sec. 2 that the function [Formula: see text] takes its maximum value on the boundary ∂Ω. This maximum principle generalizes a recent result of Ma who investigated the case f= const in R2. In Sec. 3 we investigate symmetry properties of u under specific boundary conditions or geometry of Ω.
2021 ◽
pp. 255-277
2020 ◽
Vol 28
(2)
◽
pp. 237-241
2011 ◽
Vol 61
(2)
◽
pp. 236-249
◽
2016 ◽
Vol 40
(4)
◽
pp. 2593-2605
◽
Keyword(s):