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
变分法与最优控制和偏微分方程》 2020-2021第二学期

Research interests

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.

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