本帖最后由 flyy 于 2023-5-13 07:53 编辑
令 $B=\left\{(x,y); x^2+y^2\leq 1\right\}$. 设 $f\in C^2(B)$ 为正值函数, 满足
$\frac{\partial^2\ln f}{\partial x^2}+\frac{\partial^2\ln f}{\partial y^2}\geq f^2(x,y), \forall\ (x,y)\in B. $
证明: $f(x,y)\leq \frac{2}{1-x^2-y^2}, \forall\ (x,y)\in B$.
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