We prove that if two $C^{1,1}(\unicode[STIX]{x1D6FA})$ solutions of the second boundary value problem for the generated Jacobian equation intersect in $\unicode[STIX]{x1D6FA}$ then they are the same solution. In addition, we extend this result to $C^{2}(\overline{\unicode[STIX]{x1D6FA}})$ solutions intersecting on the boundary, via an additional convexity condition on the target domain.

中文翻译：

---

生成的雅可比方程的不同解不能相交

我们证明如果两个$C^{1,1}(\unicode[STIX]{x1D6FA})$生成的雅可比方程的第二个边值问题的解相交于$\unicode[STIX]{x1D6FA}$那么它们是相同的解决方案。此外，我们将此结果扩展到$C^{2}(\overline{\unicode[STIX]{x1D6FA}})$通过目标域上的附加凸性条件，在边界上相交的解。