Yifeng Yu

Full professor, University of California at Irvine

Biography

Yifeng Yu is a Full Professor in the Department of Mathematics at the University of California, Irvine. He completed his Ph.D. in Mathematics at the University of California, Berkeley, in 2005, following his undergraduate studies in Mathematics at Nankai University, China, in 1999. Prior to joining UC Irvine, Yu held positions as an instructor at the University of Texas at Austin and as a postdoctoral fellow at the Mathematical Sciences Research Institute in Berkeley.

Yu's research focuses on partial differential equations, particularly the analysis of the infinity Laplacian and Hamilton-Jacobi equations. He has made significant contributions through his extensive publication record, which includes over 50 peer-reviewed articles in journals such as the Journal of Differential Equations and SIAM Journal on Mathematical Analysis. Yu's work has been supported by several National Science Foundation grants, including a notable NSF CAREER award for his research on the analysis of G-equations and turbulent flame speed modeling.

At UC Irvine, Yu is responsible for teaching both undergraduate and graduate courses in mathematical analysis and partial differential equations. He actively participates in the academic community by serving on various journal editorial boards and as a referee for numerous mathematical journals. Yu also contributes to the profession through his involvement as a panelist for the NSF analysis program and has been invited to speak at various national and international conferences on topics related to his research interests.

Education

PhD in Partial differential equations, U.C. Berkeley, 2005
BS in Mathematics, Nankai University, 1999

Distinctions

NSF CAREER award 1151919, 2012

Areas of Expertise

Partial Differential Equations
Infinity Laplacian
Aronsson Equation
Hamilton-Jacobi Equations
Turbulent Flame Speed Modeling
Homogenization Theory
Game Theory in PDEs
Weak KAM Theory
Viscosity Solutions
Geometric Analysis

Recent Publications

Hung Tran, “Differentiability of effective fronts in the continuous setting in two dimensions” (opens in new tab), International Mathematics Research Notices, vol. 2024, no. 7, pp. 5548–5585, 2024.
Hongwei Gao, Ziang Long, Jack Xin, “Existence of an effective burning velocity in cellular flow for curvature G-equation via game analysis” (opens in new tab), Journal of Geometric Analysis, vol. 34, pp. Article number 81, 2024.
Jack Xin, Paul Ronney, “Lagrangian game theoretic and PDE methods for averaging G-equations in turbulent combustion: existence and beyond” (opens in new tab), Bulletin of AMS, vol. 61, no. 3, pp. 470–514, 2024.
Qian J., Sprekeler T., Tran H.V., Yu Y., “OPTIMAL RATE OF CONVERGENCE IN PERIODIC HOMOGENIZATION OF VISCOUS HAMILTON-JACOBI EQUATIONS” (opens in new tab), Multiscale Modeling and Simulation, vol. 22, pp. 1558-1584, 2024.
Wenjia Jing, Hung V. Tran, “Effective fronts of polygon shapes in two dimensions” (opens in new tab), SIAM Journal on Mathematical Analysis, vol. 55, no. 6, 2023.
“High Degeneracy of Effective Hamiltonian in Two Dimensions” (opens in new tab), Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire, vol. 39, no. 1, pp. 201–223, 2022.

Most Cited Publications

L.C. Evans, “Various properties of solutions to the infinity Laplacian equation” (opens in new tab), Comm. Partial Differential Equations, vol. 30, no. 7-9, pp. 1401–1428, 2005.
Cannarsa P., Yu Y., “Singular dynamics for semiconcave functions” (opens in new tab), Journal of the European Mathematical Society, vol. 11, pp. 999-1024, 2009.
“Some properties of the infinity ground state” (opens in new tab), Indiana University Mathematics Journal, vol. 56, no. 2, pp. 947-964, 2007.
Scott Armstrong, Hung Tran, “Stochastic homogenization of a nonconvex Hamilton-Jacobi equation” (opens in new tab), Calc. Var. Partial Differential Equations, vol. 54, no. 2, pp. 1507–1524, 2015.
Jack Xin, “Periodic homogenization of inviscid G-equation for incompressible flows” (opens in new tab), Comm. Math. Sciences, vol. 8, no. 4, pp. 1067-1078, 2010.
“L ∞ variational problems and Aronsson equations” (opens in new tab), Arch. Rational. Mechanics. Anal, vol. 182, no. 1, pp. 153-180, 2006.
Scott Armstrong, Hung Tran, “Stochastic homogenization of nonconvex Hamilton-Jacobi equations in one space dimension” (opens in new tab), J. Differential Equations, vol. 261, pp. 2702–2737, 2016.
Ron Gariepy, Changyou Wang, “Generalized cone comparison principle for viscosity solutions of the Aronsson equation and absolute minimizers” (opens in new tab), Comm. Partial Differential Equations, vol. 31, no. 7-9, pp. 1027-1046, 2006.
Changyou Wang, “C 1 -boundary regularity of planar infinity harmonic functions” (opens in new tab), Math. Res. Lett., vol. 19, no. 04, pp. 823–835, 2012.
Jack Xin, “Sharp asymptotic growth laws of turbulent flame speeds in cellular flows by inviscid Hamilton-Jacobi models” (opens in new tab), Annales I’Institut H. Poincare- Analyse non lineaire, vol. 30, no. 6, pp. 1049–1068, 2013.

Contact Information

Email: yyu1@math.uci.edu

Phone: 949-824-0286

Address: University of California at Irvine

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Last updated on 2/14/2025.