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

Education

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

• Cannarsa, Piermarco; Cheng, Wei; Mazzola, Marco; Wang, Kaizhi,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.
• Cannarsa, Piermarco; Cheng, Wei; Wang, Kaizhi; Yan, Jun,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.
• 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.
• 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.
• 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
• Chen, C.; Cheng, W.; Zhang, Q.Lasry-Lions approximations for discounted Hamilton-Jacobi equations. J. Differential Equations 265 (2018), no. 2, 719-732.
• Cannarsa, P.; Cheng, W. Generalized characteristics and Lax-Oleinik operators: global theory. Calc. Var. Partial Differential Equations 56 (2017), no. 5, 56:125
• 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.
• Chen, C.; Cheng, W.Lasry-Lions, Lax-Oleinik and generalized characteristics. Sci. China Math. 59 (2016), no. 9, 1737-1752.
• Cannarsa, P.; Cheng, W.Homoclinic orbits and critical points of barrier functions. Nonlinearity 28 (2015), no. 6, 1823-1840.
• 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.
• Cheng, W.Generalized Maupertuis' principle with applications. Acta Math. Sin. (Engl. Ser.) 28 (2012), no. 11, 2153-2160.
• Cheng, W.On Mather's α-function of mechanical systems. Proc. Amer. Math. Soc. 139 (2011), no. 6, 2143-2149.
• Cheng, W.The integrability of positively definite Lagrangian systems via variational criterion: mechanical systems. J. Differential Equations 249 (2010), no. 7, 1664-1673.

Preprints

• Cannarsa, P.; Cheng, W. On and beyond propagation of singularities of viscosity solutions, arXiv:1805.11583, 2018.
• Cannarsa, P; Cheng, W.; Mendico, C.; Wang, K. Long time behavior of first order mean field games on Euclidean space, arXiv:1809.09057, 2018.
• Cannarsa, P.; Cheng, W.; Jin, L.; Wang, K.; Yan, J. Herglotz' variational principle and Lax-Oleinik evolution, arXiv:1907.05769, 2019.
• Hong, J.; Cheng, W.; Hu, S.; Zhao, K. Representation formulas for contact type Hamilton-Jacobi equations, arXiv:1907.07542, 2019.
• Cannarsa, P.; Cheng, W.; Fathi, A. Singularities of solutions of time dependent Hamilton-Jacobi equations. Applications to Riemannian geometry, arXiv:1912.04863, 2019.

Other links

• ArXiv
• MathSciNet