Yifeng Yu Email address: yifengyu@math.utexas.edu Voice Phone Number: 512-475-8145 Office: RLM 10-148 Research interest: Partial Differential Equations

My paper and preprints:

 [1]   Tangent lines of contact for the Infinity Laplacian,   Calc. Var. Partial Differential Equations 21 (2004), no. 4, 349--355 [2]   $L^{\infty}$ variational problems and Aronsson equations,  Arch. Rational. Mechanics. Anal, 182,  no1, 153-180. [3]   Various properties of solutions to the infinity Laplacian equation, (with L.C. Evans). Comm. Partial Differential Equations, 30 (2005), no. 7-9,  1401--1428. [4]  Genralized cone comparion principle for viscosity solutions of the Aronsson equation and absoute minimizers, (with Ron Gariepy, Changyou Wang), Comm. Partial Differential Equations. 31 (2006), no. 7-9, 1027-1046. [5]   Some properites of the infinity ground state, Indiana university mathematics Journal. 56 No. 2 (2007), 947–964 [6]  A remark on the semiclassical measure,  Proc. Amer. Math. Soc. 135 (2007), no.5,1449-1454. [7]  $C^1$-regularity of the Aronsson equation in $\R^2$, (with Changyou wang), to appear in Annales I'Institut H. Poincar\'e- Analyse non lin\'eaire. [8]  $L^{\infty}$ variational problems and weak KAM theory, Comm. Pure Appl. Math, Vol. 60, 1111-1147 (2007). [9]   A simple proof of the propagation of singularities for solutions of Hamilton-Jacobi equations, , Ann. Sc. Norm. Super. Pisa. Cl. Sci. (5). 2006, 439-444. [10] Singular set of a convex potential in two dimensions, to appear in Comm. Partial Differential Equations. [11] A remark on the $C^2$ solution of the infinity Laplacian equation,  Electron. J. Diff. Eqns., Vol. 2006(2006), No. 122, pp. 1-4. [12] Derivation of Aronsson equation for $C^1$ Hamiltonian, (with M.G. Crandall, Changyou Wang), to appear in Trans. Amer. Math. Soc. [13] Asymptotic behavior of  infinity harmonic functions near isolated singularity, (with Ovidius Savin, Changyou Wang), to appear in  Int. Math. Res. Not. [14] Uniqueness and Nonuniqueness of viscosity solutions of Aronsson equations, (with Robert Jensen, Changyou Wang), accepted by Arch. Rational. Mechanics. Anal. [15] uniqueness of values of Aronsson operators and applications to tug-of-war" game theory,  submitted. [16] Dynamics of propagation of singularities of semiconcave functions, (with P. Cannarsa), to appear in  J. Eur. Math. Soc (JEMS). [17] Properties of effective Hamiltonian and connections with Aubry-Mather theory in two dimension, submitted.