论文标题
关于Coifman，Lions，Meyer和Semmes的Jacobian问题的注释
A note on the Jacobian problem of Coifman, Lions, Meyer and Semmes
论文作者
论文摘要
Coifman，Lions，Meyer和Semmes在1993年询问了Jacobian操作员和其他补偿紧凑型数量是否将其自然域映射到可实现的耐力空间$ \ MATHCAL {H}^1（\ MATHBBBB {r}^n）$。在二次操作员的情况下，我们为问题提供了公理的Banach空间几何方法。我们还在主要开放式案例（飞机上的雅各布方程）上取得了进展。
Coifman, Lions, Meyer and Semmes asked in 1993 whether the Jacobian operator and other compensated compactness quantities map their natural domain of definition onto the real-variable Hardy space $\mathcal{H}^1(\mathbb{R}^n)$. We present an axiomatic, Banach space geometric approach to the problem in the case of quadratic operators. We also make progress on the main open case, the Jacobian equation in the plane.
