论文标题
hamiltonians $ h（x，p）$的rademacher型定理和对绝对最小化器的应用
A Rademacher type theorem for Hamiltonians $H(x,p)$ and application to absolute minimizers
论文作者
论文摘要
我们在非常弱的欧几里得和Carnot-Carthéodory空间中建立了涉及汉密尔顿人$ h（x，p）$的Rademacher型定理。特别是，假定$ h（x，p）$仅在变量$ x $中可以测量，并且在变量$ p $中是Quasiconvex和较低的连续性。如果没有变量$ p $的较低流行性，我们提供了一个反示例，显示了这种Rademacher型定理的失败。此外，通过应用这样的Rademacher类型定理，我们建立了对相应的$ L^\ infty $功能的绝对最小化器的存在结果。这些在文献中改善或扩展了几个已知结果。
We establish a Rademacher type theorem involving Hamiltonians $H(x,p)$ under very weak conditions in both of Euclidean and Carnot-Carathéodory spaces. In particular,$H(x,p)$ is assumed to be only measurable in the variable $x$, and to be quasiconvex and lower-semicontinuous in the variable $p$. Without the lower-semicontinuity in the variable $p$, we provide a counter example showing the failure of such a Rademacher type theorem. Moreover, by applying such a Rademacher type theorem we build up an existence result of absolute minimizers for the corresponding $L^\infty$-functional. These improve or extend several known results in the literature.
