On the Lp Monge–Ampère equation

Shibing Chen; Qi rui Li; Guangxian Zhu

doi:10.1016/j.jde.2017.06.007

On the L_p Monge–Ampère equation

Shibing Chen, Qi rui Li, Guangxian Zhu^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

77 Citations (Scopus)

Abstract

For the case where 0<p<1, we prove the existence of solutions of the L_p Monge–Ampère equation for arbitrary measures and show that the solution is in general not unique.

Original language	English
Pages (from-to)	4997-5011
Number of pages	15
Journal	Journal of Differential Equations
Volume	263
Issue number	8
DOIs	https://doi.org/10.1016/j.jde.2017.06.007
Publication status	Published - 15 Oct 2017

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10.1016/j.jde.2017.06.007

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@article{fca7648366494ebc829dad858b07506b,

title = "On the Lp Monge–Amp{\`e}re equation",

abstract = "For the case where 0p Monge–Amp{\`e}re equation for arbitrary measures and show that the solution is in general not unique.",

keywords = "L Minkowski problem, L surface area measure, Monge–Amp{\`e}re type equation",

author = "Shibing Chen and Li, \{Qi rui\} and Guangxian Zhu",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

year = "2017",

month = oct,

day = "15",

doi = "10.1016/j.jde.2017.06.007",

language = "English",

volume = "263",

pages = "4997--5011",

journal = "Journal of Differential Equations",

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T1 - On the Lp Monge–Ampère equation

AU - Chen, Shibing

AU - Li, Qi rui

AU - Zhu, Guangxian

PY - 2017/10/15

Y1 - 2017/10/15

N2 - For the case where 0p Monge–Ampère equation for arbitrary measures and show that the solution is in general not unique.

AB - For the case where 0p Monge–Ampère equation for arbitrary measures and show that the solution is in general not unique.

KW - L Minkowski problem

KW - L surface area measure

KW - Monge–Ampère type equation

UR - https://www.scopus.com/pages/publications/85021101948

U2 - 10.1016/j.jde.2017.06.007

DO - 10.1016/j.jde.2017.06.007

M3 - Article

SN - 0022-0396

VL - 263

SP - 4997

EP - 5011

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 8

ER -

On the Lp Monge–Ampère equation

Abstract

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On the L_p Monge–Ampère equation