Boundary regularity of Riesz potential, smooth solution to the chord log-Minkowski problem

2023/04/27 by Hu, Jinrong, Huang, Yong, Lu, Jian
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.14220

Abstract

The Riesz potential and its potential theory are closely related to the regularity of solutions to partial differential equations. In this paper, we investigate a class of Minkowski type problems that are closely associated with convex geometry and geometric probability. This investigation leads to a novel result regarding the boundary regularity of the Riesz potential, which is essential for developing the regularity theory of a new nonlocal Monge-Ampère equation. As an initial application, the existence of a smooth solution to the chord log-Minkowski problem shall be obtained from the perspective of a nonlocal elliptical partial differential equation and a nonlocal Gauss curvature flow equation.

Related

• The chord Gauss curvature flow and its L_p chord Minkowski problem
• The Riesz α-energy of log-concave functions and related Minkowski problem
• Flow by Gauss Curvature to the orlicz Chord Minkowski Problem
• The L_p chord Minkowski problem for super-critical exponent
• Riesz potential estimates for mixed local-nonlocal problems with measure data