- Partial Differential Equations, Calculus of Variations, Stochastic Analysis, Mean Field Games, Stochastic Differential Games, Stochastic Controls and 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:

- Partial Differential Equations, Calculus of Variations, Stochastic Analysis, Mean Field Games, Stochastic Differential Games, Stochastic Controls and Mathematical Finance.

Publications and Preprints

- Well-posedness for Hamilton-Jacobi equations in the Wasserstein space on graphs, with W. Gangbo, in preparation.
- Weak solutions of second order master equations for mean field games with common noise, with J. Zhang, in preparation.
- Weak solutions of mean field game master equtions, with J. Zhang, preprint.
- 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, Calc. Var. Partial Differential Equations 58 (2019), Paper No. 143.
- Coupling Levy measures and comparison principles for viscosity solutions, with N. Guillen and A. Swiech, to appear in Trans. Amer. Math. Soc.
- Stochastic Representations for Solutions to Parabolic Dirichlet Problems for Nonlocal Bellman Equations, with R. Gong and A. Swiech, to appear in the Annals of Applied Probability.
- Remarks on Schauder estimates and existence of classical solutions for a class of uniformly parabolic Hamilton-Jacobi-Bellman integro-PDE, J. Dynam. Differential Equations 31 (2019), 719--743.
- 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