Exterior Dirichlet Problems for Hessian Quotient Equations of Mixed Type

Yu Lei; Zhisu Li

Exterior Dirichlet Problems for Hessian Quotient Equations of Mixed Type

Analysis of PDEs 2026-08-11 v1

Authors: Yu Lei , Zhisu Li

Abstract

We study the exterior Dirichlet problem for the mixed Hessian quotient equation $\frac{\sigma_k(\eta(D^2 u))}{\sigma_l(\eta(D^2 u))} = 1,$ where $\eta(M) = (\operatorname{tr} M)I - M$ . We establish existence and uniqueness of smooth admissible solutions with prescribed quadratic asymptotics at infinity, and obtain full derivative decay of the remainder. The proof relies on a three-stage subsolution construction.

Keywords

exterior Dirichlet problem Hessian quotient equation mixed type subsolution construction derivative decay

Cite

@article{arxiv.2608.10834,
  title  = {Exterior Dirichlet Problems for Hessian Quotient Equations of Mixed Type},
  author = {Yu Lei and Zhisu Li},
  journal= {arXiv preprint arXiv:2608.10834},
  year   = {2026}
}