- Nonlinear PDE and integro PDE
- Mean field games
- Optimal transport
- Stochastic optimal control
- Stochastic differential games
- Mathematical Finance

Department of Mathematics

University of California, Los Angeles

520 Portola Plaza

Los Angeles 90095, CA, USA

Office: 5338

E-mail Address: muchenchen [at] math [dot] ucla [dot] edu

Phone: 678-296-4086

Research Interests

I am an Assistant Adjunct Professor at the Department of Mathematics of UCLA. I work under the mentorship of Prof. Wilfrid Gangbo. I graduated from Georgia Institute of Technology. I was a student of Prof. Andrzej Swiech and Prof. Yingfei Yi. My research interests are:

- Nonlinear PDE and integro PDE
- Mean field games
- Optimal transport
- Stochastic optimal control
- Stochastic differential games
- Mathematical Finance

Publications and Preprints

- Geodesic of minimal length in the set of probability measures on graphs, with W. Gangbo and W. Li, to appear in ESAIM Control Optim. Calc. Var..
- Regularity theory for second order integro-PDEs, with Y. Zhang, preprint.
- Existence of C^\alpha solutions to integro-PDEs, preprint.
- Coupling Levy measures and comparison principles for viscosity solutions, with N. Guillen and A. Swiech, preprint.
- Stochastic Representations for Solutions to Parabolic Dirichlet Problems for Nonlocal Bellman Equations, with R. Gong and A. Swiech, to appear in Annals of Applied Probability.
- Remarks on Schauder estimates and existence of classical solutions for a class of uniformly parabolic Hamilton-Jacobi-Bellman integro-PDE, to appear in J. Dynam. Differential Equations.
- Aleksandrov-Bakelman-Pucci maximum principles for a class of uniformly elliptic and parabolic integro-PDE, with A. Swiech, J. Differential Equations 264 (2018), 2708--2736.
- Perron's method for nonlocal fully nonlinear equations, Anal. PDE 10 (2017), 1227-1254.
- Interior regularity for nonlocal fully nonlinear equations with Dini continuous terms, J. Differential Equations 260 (2016), 7892--7922.
- Semiconcavity of viscosity solutions for a class of degenerate elliptic integro-differential equations in R^n, Indiana Univ. Math. J. 65 (2016), 1891-1920.
- Uniqueness of viscosity solutions for a class of integro-differential equations, with A. Swiech, NoDEA Nonlinear Differential Equations Appl. 22 (2015), 1851-1882.
- Interior regularity for regional fractional Laplacian, with Y. Yi, Comm. Math. Phys. 340 (2015), 233-251.
- Nonlinear elliptic systems involving the fractional Laplacian in the unit ball and on a half space, Commun. Pure Appl. Anal. 14 (2015), 2335-2362.

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Teaching