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Lipschitz regularity for viscous Hamilton-Jacobi equations with Lp terms
Annales de l'Institut Henri Poincaré C, Analyse non linéaire ( IF 1.8 ) Pub Date : 2020-02-04 , DOI: 10.1016/j.anihpc.2020.01.006 Marco Cirant 1 , Alessandro Goffi 2
中文翻译:
具有L p项的粘性Hamilton-Jacobi方程的Lipschitz正则性
更新日期:2020-02-04
Annales de l'Institut Henri Poincaré C, Analyse non linéaire ( IF 1.8 ) Pub Date : 2020-02-04 , DOI: 10.1016/j.anihpc.2020.01.006 Marco Cirant 1 , Alessandro Goffi 2
Affiliation
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。