论文标题

生成的雅各布方程的不同解决方案不能相交

Distinct solutions to generated Jacobian equations cannot intersect

论文作者

Rankin, Cale

论文摘要

我们证明,如果生成的jacobian方程在$ω$中相交的第二个边界值问题的两个$ c^{1,1}(ω)$解决方案,则它们是相同的解决方案。此外,我们将此结果扩展到$ c^{2}(\OverlineΩ)$ solutions通过目标域上的附加凸条件在边界上相交。

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

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