Existence and uniqueness of solutions to Orlicz Minkowski problems involving 0 < p < 1

Abstract

We establish the existence and uniqueness of positive solutions for some planar Orlicz Minkowski problems involving 0<p<1. As a consequence, the existence and uniqueness of plane convex bodies that are not origin-symmetric with 0<p<1 involved are obtained.

MSC

34B16
34C25
52A40

Keywords

Orlicz Minkowski problem
Variational method