Scott N. Armstrong

Assistant Professor
Department of Mathematics
University of Wisconsin
Madison, WI 53706

email: armstron@math.wisc.edu
office: 721 Van Vleck Hall

Curriculum Vitae | pdf

Research Interests

Nonlinear partial differential equations. Stochastic homogenization.

 

Publications and preprints

  1. (with P. E. Souganidis) Stochastic homogenization of level-set convex Hamilton-Jacobi equations. arXiv
  2. (with P. E. Souganidis) Concentration phenomena for neutronic multigroup diffusion in random environments. arXiv
  3. (with P. E. Souganidis) Stochastic homogenization of $L^\infty$ variational problems, Adv. Math., 229 (2012), no. 6, 3508-3535. arXiv | journal
  4. (with B. Sirakov and C. K. Smart) Singular solutions of fully nonlinear elliptic equations and applications, Arch. Ration. Mech. Anal., to appear. arXiv | journal
  5. (with L. Silvestre and C. K. Smart) Partial regularity of solutions of fully nonlinear uniformly elliptic equations, Comm. Pure Appl. Math., to appear. arXiv | journal
  6. (with P. E. Souganidis) Stochastic homogenization of Hamilton-Jacobi and degenerate Bellman equations in unbounded environments, J. Math. Pures Appl. (9), 97 (2012), no. 5, 460-504. arXiv | journal
  7. (with L. Silvestre) Unique continuation for fully nonlinear elliptic equations, Math. Res. Lett., 18 (2011), no. 5, 921-926. arXiv | journal
  8. (with B. Sirakov) Nonexistence of positive supersolutions of elliptic equations via the maximum principle, Comm. Partial Differential Equations, 36 (2011), no. 11, 2011-2047. arXiv | journal
  9. (with M. G. Crandall, V. Julin, and C. K. Smart) Convexity criteria and uniqueness of absolutely minimizing functions, Arch. Ration. Mech. Anal., 200 (2011), no. 2, 405-443. arXiv | journal
  10. (with B. Sirakov) Sharp Liouville results for fully nonlinear equations with power-growth nonlinearities, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 10 (2011), no. 3, 711-728. arXiv | journal
  11. (with B. Sirakov and C. K. Smart) Fundamental solutions of homogeneous fully nonlinear elliptic equations, Comm. Pure. Appl. Math., 64 (2011), no. 6, 737-777. arXiv | journal
  12. (with C. K. Smart and S. J. Somersille) An infinity Laplace equation with gradient term and mixed boundary conditions, Proc. Amer. Math. Soc., 139 (2011), no. 5, 1763-1776. arXiv | journal
  13. (with C. K. Smart) An easy proof of Jensen's theorem on the uniqueness of infinity harmonic functions, Calc. Var. Partial Differential Equations 37 (2010), 381-384. arXiv | journal
  14. (with C. K. 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. arXiv | journal
  15. (with M. Trokhimtchouk) Long-time asymptotics for fully nonlinear homogeneous parabolic equations, Calc. Var. Partial Differential Equations 38 (2010), 521-540. arXiv | journal
  16. The Dirichlet problem for the Bellman equation at resonance, J. Differential Equations 247 (2009), 931-955. arXiv | journal
  17. Principal eigenvalues and an anti-maximum principle for homogeneous fully nonlinear elliptic equations, J. Differential Equations 246 (2009), 2958-2987. arXiv | journal
  18. (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
  19. (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