Uniqueness of least energy solutions for Monge–Ampère functional

Genggeng Huang*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    2 Citations (Scopus)

    Abstract

    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.

    Original languageEnglish
    Article number73
    JournalCalculus of Variations and Partial Differential Equations
    Volume58
    Issue number2
    DOIs
    Publication statusPublished - 1 Apr 2019

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