$C^{1, 1}$ regularity for solutions to the degenerate $L_p$ Dual Minkowski problem

Abstract

In this paper, we study $C^{1, 1}$ regularity for solutions to the degenerate $L_p$ Dual Minkowski problem. Our proof is motivated by the idea of Guan and Li's work on $C^{1,1}$ estimates for solutions to the Aleksandrov problem.