Lorentz-Minkowski空间R_(1)^(n+1)中一类Hessian商方程的Dirichlet问题

The Dirichlet Problem for a Class of Hessian Quotient Equations in Lorentz-Minkowski Space R_(1)^(n+1)

在适当的假设条件下,本文给出了(n+1)-维Lorentz-Minkowski空间R_(1)^(n+1)中一类带有Dirichlet边值条件的Hessian商方程解的存在唯一性.事实上,该方程可以看作一类预定曲率问题,同时也是工作[Mathematische Nachrichten,2024,297:833-860]的延续.

In this paper,under suitable settings,we can obtain the existence and uniqueness of solutions to a class of Hessian quotient equations with Dirichlet boundary condition in Lorentz-Minkowski space R_(1)^(n+1),which can be seen as a prescribed curvature problem and a continuous work of[Mathematische Nachrichten,2024,297:833-860].