TY - JOUR
T1 - Uniqueness of least energy solutions for Monge–Ampère functional
AU - Huang, Genggeng
N1 - Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/4/1
Y1 - 2019/4/1
N2 - Let Ω be a bounded, smooth, uniformly convex domain in R n . We consider the following functional E[u]=∫Ω(-u)detD2udx,‖u‖Lq+1(Ω)=1(0.1)where u∈ C 2 (Ω ¯) is convex and u= 0 on ∂Ω. In this paper, the uniqueness of least energy solution of (0.1) is investigated. For n= 2 , we prove the least energy solution of (0.1) is unique for 2 < q< ∞ provided it is locally uniformly convex. In particular, for q= + ∞, we show the uniqueness of the least energy solution of (0.1) and find its relation to Santalò point.
AB - Let Ω be a bounded, smooth, uniformly convex domain in R n . We consider the following functional E[u]=∫Ω(-u)detD2udx,‖u‖Lq+1(Ω)=1(0.1)where u∈ C 2 (Ω ¯) is convex and u= 0 on ∂Ω. In this paper, the uniqueness of least energy solution of (0.1) is investigated. For n= 2 , we prove the least energy solution of (0.1) is unique for 2 < q< ∞ provided it is locally uniformly convex. In particular, for q= + ∞, we show the uniqueness of the least energy solution of (0.1) and find its relation to Santalò point.
UR - http://www.scopus.com/inward/record.url?scp=85063352285&partnerID=8YFLogxK
U2 - 10.1007/s00526-019-1504-5
DO - 10.1007/s00526-019-1504-5
M3 - Article
SN - 0944-2669
VL - 58
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 2
M1 - 73
ER -