Minkowski problem arising from sub-linear elliptic equations

2022/02/06 by Yi Xing, Qiuyi, Dai, Xing, Yi
Computer Science · Mathematics · #35J92 35N25 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2202.02808

openalex publication_date 2022/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any bounded convex domain Ωin R^N, we assign a positive finite Borel measure associated with the solution to a su-blinear elliptic equation in Ω. We prove that this measure is weakly continuous in the sense of measure with respect Hausdorff metric, and the Minkowski problem associated with this measure is uniquely solvable.

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