Minkowski problem arising from sub-linear elliptic equations

Dai Qiuyi; Yi Xing

Minkowski problem arising from sub-linear elliptic equations

Analysis of PDEs 2022-02-09 v2

Authors: Dai Qiuyi , Yi Xing

Abstract

For any bounded convex domain \Omega in R^N, we assign a positive finite Borel measure associated with the solution to a su-blinear elliptic equation in \Omega. 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.

Keywords

elliptic partial differential equations measure theory bounded domains

Cite

@article{arxiv.2202.02808,
  title  = {Minkowski problem arising from sub-linear elliptic equations},
  author = {Dai Qiuyi and Yi Xing},
  journal= {arXiv preprint arXiv:2202.02808},
  year   = {2022}
}