论文标题
路径汉密尔顿 - 雅各比方程的插值结果
Interpolation results for pathwise Hamilton-Jacobi equations
论文作者
论文摘要
我们通过使用插值方法研究路径规则与汉密尔顿 - 雅各比方程理论的规律性之间的相互作用。相对于Sobolev，Besov，Hölder和变异规范来衡量路径的规律性，并以规律性和结构来呈现Hamiltonians的标准。我们还探索了可表示为凸函数差的函数的各种特性，这是哈密顿量最大的空间，该方程在所有连续路径上都符合方程式。最后，我们讨论一些开放的问题和猜想。
We study the interplay between the regularity of paths and Hamiltonians in the theory of pathwise Hamilton-Jacobi equations with the use of interpolation methods. The regularity of the paths is measured with respect to Sobolev, Besov, Hölder, and variation norms, and criteria for the Hamiltonians are presented in terms of both regularity and structure. We also explore various properties of functions that are representable as the difference of convex functions, the largest space of Hamiltonians for which the equation is well-posed for all continuous paths. Finally, we discuss some open problems and conjectures.
