Charles K. Smart

Assistant Professor

smart@math.cornell.edu

401 Malott Hall
Department of Mathematics
Cornell University
Ithaca, NY 14853-4201

Teaching

I am currently teaching Math 6140 Viscosity Solutions.

Research

I study nonlinear partial differential equations and probability. My research is partially supported by the National Science Foundation and the Sloan Foundation. The following is a list of my preprints and publications.

• Armstrong and Smart, Quantitative stochastic homogenization of convex integral functionals, preprint.
• Lee, Peres, and Smart, A Gaussian upper bound for martingale small-ball probabilities, preprint.
• Levine, Pegden, and Smart, The Apollonian structure of integer superharmonic matrices, preprint.
• Armstrong and Smart, Quantitative stochastic homogenization of elliptic equations in nondivergence form , preprint.
• Armstrong and Smart, Stochastic homogenization of fully nonlinear elliptic uniformly elliptic equations revisited, preprint.
• Levine, Pegden, and Smart, Apollonian Structure in the Abelian Sandpile, preprint.
• Armstrong and Smart, Regularity and stochastic homogenization of fully nonlinear equations without uniform ellipticity, Ann. Prob., to appear.
• Hynd, Smart, and Yu, Nonuniqueness of infinity ground states, Calc. Var. Partial Differential Equations, to appear.
• Pegden and Smart, Convergence of the Abelian sandpile, Duke Math. J., to appear.
• Armstrong, Sirakov, and Smart, Singular solutions of fully nonlinear elliptic equations and applications, Arch. Ration. Mech. Anal. 205 (2012), no. 2, 345-394.
• Armstrong and Silvestre, Partial regularity of solutions of fully nonlinear uniformly elliptic equations, Comm. Pure Appl. Math. 65 (2012), no. 8, 1169-1184.
• Evans and Smart, Adjoint methods for the infinity Laplacian PDE, Arch. Ration. Mech. Anal. 201 (2011), no. 1, 87-113.
• Evans and Smart, Everywhere differentiability of infinity harmonic functions, Calc. Var. Partial Differential Equations 42 (2011), no. 1-2, 289-299.
• Sheffield and Smart, Vector-valued optimal Lipschitz extensions, Comm. Pure. Appl. Math. 65 (2012), no. 1, 128-154..
• Armstrong, Crandall, Julin, and Smart, Convexity criteria and uniqueness of absolutely minimizing functions, Arch. Ration. Mech. Anal., 200 (2011), no. 2, 405-443.
• Armstrong and Sirakov, Fundamental solutions of homogeneous fully nonlinear elliptic equations, Comm. Pure. Appl. Math., 64 (2011), no. 6, 737-777.
• Armstrong and Somersille, An infinity Laplace equation with gradient term and mixed boundary conditions, Proc. Amer. Math. Soc., 139 (2011), no. 5, 1763--1776.
• Armstrong and Smart, An easy proof of Jensen's theorem on the uniqueness of infinity harmonic functions, Calc. Var. Partial Differential Equations 37 (2010), 381-384.
• Armstrong and Smart, A finite difference approach to the infinity Laplace equation and tug-of-war games, Trans. Amer. Math. Soc. 364 (2012), no. 2, 595-636.
• Smart, Interpreting Hasson's example, draft.