$C^{1, 1}$ regularity for solutions to the degenerate $L_p$ Dual Minkowski problem
Li Chen, Qiang Tu, Di Wu, Ni Xiang
TL;DR
This paper establishes $C^{1,1}$ regularity for solutions to the degenerate $L_p$ Dual Minkowski problem, extending regularity results in convex geometric analysis.
Contribution
It provides the first $C^{1,1}$ regularity results for solutions to the degenerate $L_p$ Dual Minkowski problem, inspired by techniques from Aleksandrov problem studies.
Findings
Proved $C^{1,1}$ regularity for degenerate solutions
Extended regularity theory to a new class of Minkowski problems
Built on Guan and Li's methods for Aleksandrov problem
Abstract
In this paper, we study regularity for solutions to the degenerate Dual Minkowski problem. Our proof is motivated by the idea of Guan and Li's work on estimates for solutions to the Aleksandrov problem.
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Taxonomy
TopicsPoint processes and geometric inequalities · Geometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations