This webpage is no longer current. I have moved to Louisiana State University. My new webpage is here, and my new email address is armstrong@math.lsu.edu. Please update your bookmarks, etc.
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 favorites are the Bellman equation and the infinity Laplace equation.
(with C. K. Smart) An easy proof of Jensen's theorem on the uniqueness of infinity harmonic functions, Calc. Var. Partial Differential Equations (to appear). preprint | arXiv
(with C. K. Smart) A finite difference approach to the infinity Laplace equation and tug-of-war games. preprint | arXiv
(with M. Trokhimtchouk) Long-time asymptotics for fully nonlinear homogeneous parabolic equations. preprint | arXiv
The Dirichlet problem for the Bellman equation at resonance, J. Differential Equations 247 (2009) 931--955. preprint | arXiv | journal
Principal eigenvalues and an anti-maximum principle for homogeneous fully nonlinear elliptic equations, J. Differential Equations 246 (2009) 2958--2987. preprint | arXiv | journal
(with C. J. Hillar) Solvability of symmetric word equations in positive definite letters, J. Lond. Math. Soc. (2) 76 (2007), no. 3, 777--796. pdf | maple file | maple file 2
(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. pdf | ps
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.
Last Updated: August 14, 2009 19:42 PT