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Exterior Dirichlet Problems for Hessian Quotient Equations of Mixed Type

Yu Lei, Zhisu Li

math.AParXiv:2608.10834

Abstract

We study the exterior Dirichlet problem for the mixed Hessian quotient equation \[ σk(η(D2 u))σl(η(D2 u)) = 1, \] where η(M) = (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.

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