Elsevier

Journal of Differential Equations

Volume 263, Issue 6, 15 September 2017, Pages 3230-3243
Journal of Differential Equations

On the 2-dimensional dual Minkowski problem

https://doi.org/10.1016/j.jde.2017.04.033Get rights and content
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Abstract

We study the 2-dimensional dual Minkowski problem, which is the following nonlinear problem on unit circleu+u=g(θ)u1(u2+u2)(2k)/2,θS, for any given positive continuous function g(θ) with 2π/m-periodic. We prove that it is solvable for all k(1,+) and m{3,4,5}.

MSC

52A38
35J15
35J96

Keywords

Dual Minkowski problem
Lp-Minkowski problem
Monge–Ampère equation

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