发表机构
School of Mathematical Sciences, Peking University（北京大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明三维次临界特殊拉格朗日方程半凸粘性解梯度图面积最小且光滑，并推广至更高维度，推进了Wang-Yuan猜想。
AI 中文摘要
我们证明了三维次临界特殊拉格朗日方程的任意$W^{2,1}$半凸粘性解的梯度图是面积最小且光滑的。此外，我们证明了$W^{2,1}\cap C^{1,1/3+}$半凸粘性解的光滑性。这推进了Wang--Yuan [WY13]提出的猜想。更高维度的相应结果也已建立。
英文摘要
We prove that the gradient graph of any $W^{2,1}$ semi-convex viscosity solution to the three-dimensional subcritical special Lagrangian equation is area-minimizing and smooth. Furthermore, we prove the smoothness of $W^{2,1}\cap C^{1,1/3+}$ semi-convex viscosity solutions. This yields progress on the conjecture proposed by Wang--Yuan [WY13]. The corresponding results in higher dimensions are also established.
Comments14 pages, comments are welcome
