# 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） 2021-2022第一学期 习题

## 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 & Optimal transport
• 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.; Fathi, A.; Singularities of solutions of time dependent Hamilton-Jacobi equations. Applications to Riemannian geometry. Publ. Math. Inst. Hautes Études Sci. 133 (2021), no. 1, 327–366.
2. Cannarsa, P.; Cheng, W.; Local singular characteristics on $$\mathbb{R}^2$$. Boll. Unione Mat. Ital. 14 (2021), no. 3, 483–504.
3. Cannarsa, P.; Cheng, W., Singularities of Solutions of Hamilton–Jacobi Equations. Milan J. Math. 89 (2021), no. 1, 187-215.
4. Cannarsa, P.; Cheng, W., On and beyond propagation of singularities of viscosity solutions. Proceedings of the International Consortium of Chinese Mathematicians 2017, 141–157, Int. Press, Boston, MA, 2020.
5. 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.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.
12. Chen, C.; Cheng, W.; Zhang, Q., Lasry-Lions approximations for discounted Hamilton-Jacobi equations. J. Differential Equations 265 (2018), no. 2, 719-732.
13. Cannarsa, P.; Cheng, W., Generalized characteristics and Lax-Oleinik operators: global theory. Calc. Var. Partial Differential Equations 56 (2017), no. 5, 56:125.
14. 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.
15. Chen, C.; Cheng, W., Lasry-Lions, Lax-Oleinik and generalized characteristics. Sci. China Math. 59 (2016), no. 9, 1737-1752.
16. Cannarsa, P.; Cheng, W., Homoclinic orbits and critical points of barrier functions. Nonlinearity 28 (2015), no. 6, 1823-1840.
17. 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.
18. Cheng, W., Generalized Maupertuis' principle with applications. Acta Math. Sin. (Engl. Ser.) 28 (2012), no. 11, 2153-2160.
19. Cheng, W., On Mather's $$\alpha$$-function of mechanical systems. Proc. Amer. Math. Soc. 139 (2011), no. 6, 2143-2149.
20. 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. Hong, J.; Cheng, W.; Hu, S.; Zhao, K., Representation formulas for contact type Hamilton-Jacobi equations, arXiv:1907.07542, 2019.
2. 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.
3. Cheng, W. and Hong, J., Local strict singular characteristics: Cauchy problem with smooth initial data, preprint, arXiv:2103.06217, 2021.

## Conference

1. VIII Partial differential equations, optimal design and numerics, Aug 18-30, 2019, Centro de Ciencias de Benasque Pedro Pascual, Benasque, Spain.
2. Conference on PDEs, Dynamical Systems and Probability, February 21-22, 2019, Kodaira, Japan.
3. CIMPA school on dynamical systems, October 25 - November 6, 2018, Kathmandu, Nepal.
4. The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, July 5-9, 2018, Taipei.
5. Gran Sasso Science Institute (GSSI) workshop on New trends in control of evolution system'', April 19-21, 2018, L'Aquila, Italy.
6. Gran Sasso Science Institute (GSSI) workshop on New developments on Hamilton-Jacobi Equations, Mean Field Games, and Weak KAM Theory'', March 2-3, 2018, L'Aquila, Italy.
7. The first annual meeting of International Consortium of Chinese Mathematicians, December 27-29, 2017, Guangzhou, China.
8. International Conference on Singularity Theory and Dynamical Systems - in Memory of John Mather, December 11-15, 2017, Sanya, China.
9. 2017 Chengdu workshop on differential dynamical systems, December, 8-20, 2017, Chengdu, China.
10. SIAM Conference on Control and Its Applications, July 10-12, 2017, Pittsburgh, Pennsylvania, US.
11. New trends in Control Theory and PDEs, Istituto Nazionale di Alta Matematica (INdAM), July 3-7, 2017, Rome, Italy.
12. Beyond Hamilton-Jacobi, Last call to Bordeaux, January, 9-13, 2017, Bordeaux, France.
13. SIAM conference on Analysis of partial Differential Equations, December, 2015, Scottsdale, Arizona, US.
14. INdAM Workshop "Hamilton-Jacobi equation: at the crossroads of PDE, Dynamical Systems and Geometry", June, 2015, Cortona, Italy.
15. Workshop on Hamiltonian dynamical systems, January, 2015, Shanghai, China.
16. International Congress of Chinese Mathematicians, July, 2013, Taipei.
17. Conference on Dynamics and Transport in Disordered Systems, June, 2011, Toronto, Canada.
18. 12th Frontier Science Symposium, November, 2011, Singapore.

## Slides

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