# Wei Cheng's homepage

Wei Cheng （程伟）

Professor of Mathematics
Department of Mathematics
Nanjing University

Contact Information:
E-mail: chengwei(at)nju.edu.cn

## Teaching Schedule:

《实变函数》（鼓楼、仙林） 2020-2021第一学期

## Research interests

• Hamiltonian dynamical systems: Mather theory and weak KAM theory
• Hamilton-Jacobi equation: viscosity solutions, regularity
• Calculus of variations and optimal control
• Mean field games
• Riemannian and sub-Riemannian geometry
• Nonsmooth analysis and geometric measure theory

## Education

Ph. D., Mathematics, Nanjing University, 1999.
B.S., Mathematics, Nanjing University, 1994.

## Publications (2010-)

1. Cannarsa, P.; Cheng, W.; Jin, L.; Wang, K.; Yan, J., Herglotz' variational principle and Lax-Oleinik evolution. J. Math. Pures Appl. (9) 141 (2020), 99–136.
2. Cannarsa, P.; Cheng, W.; Mendico, C.; Wang, K., Long-Time Behavior of First-Order Mean Field Games on Euclidean Space. Dyn. Games Appl. 10 (2020), no. 2, 361-390.
3. Cannarsa, P.; Cheng, W.; Mazzola, M.; Wang, K., Global Generalized Characteristics for the Dirichlet Problem for Hamilton–Jacobi Equations at a Supercritical Energy Level. SIAM J. Math. Anal. 51 (2019), no. 5, 4213-4244.
4. Cannarsa, P.; Cheng, W.; Wang, K.; Yan, J., Herglotz' generalized variational principle and contact type Hamilton-Jacobi equations. Trends in control theory and partial differential equations, 39-67, Springer INdAM Ser., 32, Springer, Cham, 2019.
5. Chen, Q.; Cheng, W.; Ishii, H.; Zhao, K., Vanishing contact structure problem and convergence of the viscosity solutions. Comm. Partial Differential Equations 44 (2019), no. 9, 801-836.
6. Cannarsa, P.; Chen, Q.; Cheng, W., Dynamic and asymptotic behavior of singularities of certain weak KAM solutions on the torus. J. Differential Equations 267 (2019), no. 4, 2448-2470.
7. Zhao, K..; Cheng, W., On the vanishing contact structure for viscosity solutions of contact type Hamilton-Jacobi equations I: Cauchy problem. Discrete Contin. Dyn. Syst. 39 (2019), no. 8, 4345-4358.
8. Chen, C.; Cheng, W.; Zhang, Q., Lasry-Lions approximations for discounted Hamilton-Jacobi equations. J. Differential Equations 265 (2018), no. 2, 719-732.
9. Cannarsa, P.; Cheng, W., Generalized characteristics and Lax-Oleinik operators: global theory. Calc. Var. Partial Differential Equations 56 (2017), no. 5, 56:125.
10. Cannarsa, P.; Cheng, W.; Fathi, A., On the topology of the set of singularities of a solution to the Hamilton-Jacobi equation. C. R. Math. Acad. Sci. Paris 355 (2017), no. 2, 176-180.
11. Chen, C.; Cheng, W., Lasry-Lions, Lax-Oleinik and generalized characteristics. Sci. China Math. 59 (2016), no. 9, 1737-1752.
12. Cannarsa, P.; Cheng, W., Homoclinic orbits and critical points of barrier functions. Nonlinearity 28 (2015), no. 6, 1823-1840.
13. Cannarsa, P.; Cheng, W.; Zhang, Q., Propagation of singularities for weak KAM solutions and barrier functions. Comm. Math. Phys. 331 (2014), no. 1, 1-20.
14. Cheng, W., Generalized Maupertuis' principle with applications. Acta Math. Sin. (Engl. Ser.) 28 (2012), no. 11, 2153-2160.
15. Cheng, W., On Mather's $$\alpha$$-function of mechanical systems. Proc. Amer. Math. Soc. 139 (2011), no. 6, 2143-2149.
16. Cheng, W., The integrability of positively definite Lagrangian systems via variational criterion: mechanical systems. J. Differential Equations 249 (2010), no. 7, 1664-1673.

## Preprints

1. Cannarsa, P.; Cheng, W., On and beyond propagation of singularities of viscosity solutions, arXiv:1805.11583, 2018.
2. Hong, J.; Cheng, W.; Hu, S.; Zhao, K., Representation formulas for contact type Hamilton-Jacobi equations, arXiv:1907.07542, 2019.
3. Cannarsa, P.; Cheng, W.; Fathi, A., Singularities of solutions of time dependent Hamilton-Jacobi equations. Applications to Riemannian geometry, arXiv:1912.04863, 2019.
4. Cannarsa, P; Cheng, W.; Mendico, C.; Wang, K., Weak KAM approach to first-order Mean Field Games with state constraints, preprint, arXiv:2004.06505, 2020.
5. Cannarsa, P.; Cheng, W., Local singular characteristics on $$\mathbb{R}^2$$, preprint, arXiv:2008.05985, 2020.
6. Cannarsa, P.; Cheng, W., Singularities of solutions of Hamilton-Jacobi equations, preprint, arXiv:2101.02075, 2021.

## Slides

1. $$\mathbb{R}^2$$上的奇性特征线，上海交通大学，2020年5月.