We provide Lipschitz regularity for solutions to viscous time-dependent Hamilton-Jacobi equations with right-hand side belonging to Lebesgue spaces. Our approach is based on a duality method, and relies on the analysis of the regularity of the gradient of solutions to a dual (Fokker-Planck) equation. Here, the regularizing effect is due to the non-degenerate diffusion and coercivity of the Hamiltonian in the gradient variable.

中文翻译：

---

具有L ^p项的粘性Hamilton-Jacobi方程的Lipschitz正则性

我们提供Lipschitz正则性，用于解决带粘滞时间的Hamilton-Jacobi方程的解决方案，其中右手侧属于Lebesgue空间。我们的方法基于对偶方法，并且依赖于对偶（Fokker-Planck）方程解的梯度正则性的分析。在此，正则化效果是由于梯度变量中哈密顿量的非简并扩散和矫顽力所致。