Global Hölder estimates for linearized Monge-Ampère equations in divergence form with applications to dual semigeostrophic equations and periodic homogenization

@misc{cui2026global,
  title = {{Global Hölder estimates for linearized Monge-Ampère equations in divergence form with applications to dual semigeostrophic equations and periodic homogenization}},
  author = {Guoqing Cui and Chong Gu and Nam Q. Le and Ling Wang and Bin Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.02071},
  eprint = {2610.02071},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.02071},
}

TY  - UNPB
TI  - Global Hölder estimates for linearized Monge-Ampère equations in divergence form with applications to dual semigeostrophic equations and periodic homogenization
AU  - Guoqing Cui
AU  - Chong Gu
AU  - Nam Q. Le
AU  - Ling Wang
AU  - Bin Zhou
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.02071
UR  - https://arxiv.org/abs/2610.02071
AB  - We establish interior and global Hölder estimates for linearized Monge-Ampère equations in divergence form in all dimensions n≥ 3, when the Hessian determinant of the convex Monge-Ampère potential is bounded above and below by positive constants and the vector field on the right-hand side is bounded. The estimates use the L^p norm of the solution for any p>1. A key ingredient is an L^1 estimate, with appropriate decay rates, for the gradient of the Green's function of the linearized Monge-Ampère operator in small sections, uniform with respect to the pole. As applications, we obtain uniform Hölder estimates for the time derivatives of the primal and dual potentials in the three-dimensional periodic dual semigeostrophic system when the initial density is bounded away from zero and infinity, and establish a linear convergence rate for periodic homogenization of the Monge-Ampère equation.
ER  -