Office: 280 Lockett Hall
Office hours: Tuesdays 3:00-4:00pm, Wednesdays 12:30-2:00pm
Email: armstrong@math.lsu.edu
Office: 280 Lockett Hall
Office hours: Tuesdays 3:00-4:00pm, Wednesdays 12:30-2:00pm
Ph.D. University of California, Berkeley, 2009
B.S. Texas A&M University, 2002
I study nonlinear elliptic and parabolic partial differential equations, and their applications. I am particularly interested in maximum principle methods for non-divergence form equations, and PDE which arise in probability theory. Two of my specific interests are the Bellman equation and the infinity Laplace equation.
[9] (with B. Sirakov and C. K. Smart) Fundamental solutions of homogeneous fully nonlinear elliptic equations, preprint. arXiv
[8] (with C. K. Smart and S. J. Somersille) An infinity Laplace equation with gradient term and mixed boundary conditions, preprint. arXiv
[7] (with C. K. Smart) An easy proof of Jensen's theorem on the uniqueness of infinity harmonic functions, Calc. Var. Partial Differential Equations, in press. arXiv | journal
[6] (with C. K. Smart) A finite difference approach to the infinity Laplace equation and tug-of-war games, preprint. arXiv
[5] (with M. Trokhimtchouk) Long-time asymptotics for fully nonlinear homogeneous parabolic equations, Calc. Var. Partial Differential Equations, in press. arXiv | journal
[4] The Dirichlet problem for the Bellman equation at resonance, J. Differential Equations 247 (2009) 931--955. arXiv | journal
[3] Principal eigenvalues and an anti-maximum principle for homogeneous fully nonlinear elliptic equations, J. Differential Equations 246 (2009) 2958--2987. arXiv | journal
[2] (with C. J. Hillar) Solvability of symmetric word equations in positive definite letters, J. Lond. Math. Soc. (2) 76 (2007), no. 3, 777--796. arxiv | journal | maple file | maple file 2
[1] (With K. Dykema, R. Exel and H. Li) On embeddings of full amalgamated free product $C*$-algebras, Proc. Amer. Math. Soc. 132 (2004), no. 7, 2019--2030. arxiv | journal
A list of all of my preprints can be found on the arXiv here.
(with C. K. Smart) A finite difference approach to the infinity Laplace equation and tug-of-war games, Workshop on New Connections Between Differential and Random Turn Games, PDEs and Image Processing, PIMS/ University of British Columbia (30 July 2009). slides
Principal half-eigenvalues of fully nonlinear homogeneous elliptic operators, Ph.D. Thesis, University of California, Berkeley, (2009). pdf. My thesis advisor was Lawrence C. Evans.
Fall 2009: Math 2065 (Elementary Differential Equations)
Last Updated: November 20, 2009 16:08 CT