The intrinsic Hopf-Lax semigroup vs. The intrinsic slope

Non-symmetric intrinsic Hopf-Lax semigroup vs. intrinsic Lagrangian

In this paper, we analyze the 'symmetrized' of the intrinsic Hopf-Lax semigroup introduced by the author in the context of the intrinsically Lipschitz sections in the setting of metric spaces. Indeed, in the usual case, we have that $d(x,y) =d(y,x)$ for any point $x$ and $y$ belong to the metric space $X$; on the other hand, in our intrinsic context, we have that $d(f(x),π^{-1} (y)) \ne d(f(y),π^{-1} (x)),$ for every $x,y \in X$. Therefore, it is not trivial that we get the same result obtained for the "classical" intrinsic Hopf-Lax semigroup, i.e., the 'symmetrized' Hopf-Lax semigroup is a su…

含 Caputo 时间分数阶导数的 Hamilton-Jacobi 方程

Hamilton-Jacobi equations involving a Caputo time-fractional derivative

本文研究含 Caputo 时间分数阶导数的 Hamilton-Jacobi 方程，证明其下解满足内在 Hopf-Lax 型表示公式。