摘要：考虑一个问题： Alexandrov weak solution $det(D^2u)=1$ in $\Omega$; $u=0$ on $\partial\Omega$. 此处$\Omega$是一个正规凸区域，即除了凸以外还满足$B_{\frac{1}{n}}\subset\Omega\subse 阅读全文

摘要：一个自然的问题给定一个$n$维$C^1$向量$\vec{A}(x)$, 能否找到一个位势函数$u$使得， $\nabla u=\vec{A}$? 当$\forall i\neq j$, $\frac{\partial A_{i}(x)}{\partial x_j}=\frac{\partial A_ 阅读全文

摘要：Elementary inequalities for $\sigma_k$ function (Lecture given by Xinan Ma)The elementary symmetric functions appear naturally in the geometric quanti 阅读全文

摘要：Book: A. Figalli 《The Monge Ampere Equation and Its Application》 1.Let $A,B\in R^{n\times n}$, and assume that $A$ is invertible. Then, $$\frac{d}{dt} 阅读全文