Preprints

  1. S. Armstrong, A. Bordas and J.-C. Mourrat. Quantitative stochastic homogenization and regularity theory of parabolic equations. arXiv

Book

  1. S. Armstrong, T. Kuusi and J.-C. Mourrat. Quantitative stochastic homogenization and large-scale regularity. arXiv | pdf (The latter is more current: last updated September 4, 2017.)

Articles

  1. S. Armstrong and P. Dario. Elliptic regularity and quantitative homogenization on percolation clusters. Comm. Pure Appl. Math., to appear. arXiv
  2. S. Armstrong, T. Kuusi, J.-C. Mourrat and C. Prange. Quantitative analysis of boundary layers in periodic homogenization. Arch. Ration. Mech. Anal., 226 (2017), 695-741. arXiv | journal
  3. S. Armstrong and J. Lin. Optimal quantitative estimates in stochastic homogenization for elliptic equations in nondivergence form. Arch. Ration. Mech. Anal., 225 (2017), 937-991. arXiv | journal
  4. S. Armstrong, T. Kuusi and J.-C. Mourrat. The additive structure of elliptic homogenization. Invent. Math., 208 (2017), 999-1154. arXiv | journal
  5. S. Armstrong, A. Gloria and T. Kuusi. Bounded correctors in almost periodic homogenization. Arch. Ration. Mech. Anal., 222 (2016), 393-426. arXiv | journal
  6. S. Armstrong, T. Kuusi and J.-C. Mourrat. Mesoscopic higher regularity and subadditivity in elliptic homogenization. Comm. Math. Phys., 347 (2016), 315-361. arXiv | journal
  7. S. Armstrong and J.-P. Daniel. Calderón-Zygmund estimates for stochastic homogenization. J. Functional Anal., 270 (2016), 312-329. arXiv | journal
  8. S. Armstrong and P. Cardaliaguet. Stochastic homogenization of quasilinear Hamilton-Jacobi equations and geometric motions. J. Eur. Math. Soc., to appear. arXiv
  9. S. N. Armstrong and J.-C. Mourrat. Lipschitz regularity for elliptic equations with random coefficients. Arch. Ration. Mech. Anal., 219 (2016), 255-348. arXiv | journal
  10. S. N. Armstrong, H. V. Tran and Y. Yu. Stochastic homogenization of nonconvex Hamilton-Jacobi equations in one space dimension. J. Differential Equations, 261 (2016), 2702-2737. arXiv | journal
  11. S. N. Armstrong and Z. Shen. Lipschitz estimates in almost-periodic homogenization. Comm. Pure Appl. Math., 69 (2016), 1882-1923. arXiv | journal
  12. S. N. Armstrong and C. K. Smart. Quantitative stochastic homogenization of convex integral functionals. Ann. Sci. Éc. Norm. Supér., 48 (2016), 423-481. arXiv | journal. This paper received the 2017 SIAG/APDE Prize for most outstanding paper in PDE.
  13. S. N. Armstrong and O. Zeitouni. Local asymptotics for controlled martingales. Ann. Appl. Probab., 26 (2016), 1467-1494. arXiv | journal
  14. S. N. Armstrong, H. V. Tran and Y. Yu. Stochastic homogenization of a nonconvex Hamilton-Jacobi equation. Calc. Var. Partial Differential Equations, 54 (2015), 1507-1524. arXiv | journal
  15. S. N. Armstrong and P. Cardaliaguet. Quantitative stochastic homogenization of viscous Hamilton-Jacobi equations, Comm. PDE, 40 (2015), 540-600. arXiv | journal
  16. S. N. Armstrong and H. V. Tran. Stochastic homogenization of viscous Hamilton-Jacobi equations and applications, Anal. & PDE, 7-8 (2014), 1969-2007. arXiv | journal
  17. S. N. Armstrong and H. V. Tran. Viscosity solutions of general viscous Hamilton-Jacobi equations, Math. Ann., 361 (2015), 647-687. arXiv | journal
  18. S. N. Armstrong and C. K. Smart. Quantitative stochastic homogenization of elliptic equations in nondivergence form, Arch. Ration. Mech. Anal., 214 (2014), 867-911. arXiv | journal
  19. S. N. Armstrong, S. Serfaty and O. Zeitouni. Remarks on a constrained optimization problem for the Ginibre ensemble, Potential Anal. 41 (2014), 945-958. arXiv | journal
  20. S. N. Armstrong and C. K. Smart. Stochastic homogenization of fully nonlinear uniformly elliptic equations revisited, Calc. Var. Partial Differential Equations 50 (2014), 967-980. arXiv | journal
  21. S. N. Armstrong and C. K. Smart. Regularity and stochastic homogenization of fully nonlinear equations without uniform ellipticity, Ann. Probab., 42 (2014), 2558-2594. arXiv | journal
  22. S. N. Armstrong, P. Cardaliaguet and P. E. Souganidis. Error estimates and convergence rates for the stochastic homogenization of Hamilton-Jacobi equations, J. Amer. Math. Soc., 27 (2014), 479-540. arXiv | journal
  23. S. N. Armstrong and P. E. Souganidis. Stochastic homogenization of level-set convex Hamilton-Jacobi equations, Int. Math. Res. Not., 2013 (2013), 3420-3449. arXiv | journal
  24. S. N. Armstrong and P. E. Souganidis. Concentration phenomena for neutronic multigroup diffusion in random environments, Ann. Inst. H. Poincaré Anal. Non Linéaire, 30 (2013), 419-439. arXiv | journal
  25. S. N. Armstrong and P. E. Souganidis. Stochastic homogenization of $L^\infty$ variational problems, Adv. Math., 229 (2012), no. 6, 3508-3535. arXiv | journal
  26. S. N. Armstrong, B. Sirakov and C. K. Smart. Singular solutions of fully nonlinear elliptic equations and applications, Arch. Ration. Mech. Anal., 205 (2012), no. 2, 345-394. arXiv | journal
  27. S. N. Armstrong, L. Silvestre and C. K. Smart. Partial regularity of solutions of fully nonlinear uniformly elliptic equations, Comm. Pure Appl. Math., 65 (2012), no. 8, 1169-1184. arXiv | journal
  28. S. N. Armstrong and 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
  29. S. N. Armstrong and L. Silvestre. Unique continuation for fully nonlinear elliptic equations, Math. Res. Lett., 18 (2011), no. 5, 921-926. arXiv | journal
  30. S. N. Armstrong and B. Sirakov. Nonexistence of positive supersolutions of elliptic equations via the maximum principle, Comm. PDE, 36 (2011), no. 11, 2011-2047. arXiv | journal
  31. S. N. Armstrong, 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
  32. S. N. Armstrong and 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
  33. S. N. Armstrong, 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
  34. S. N. Armstrong, 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
  35. S. N. Armstrong and 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
  36. S. N. Armstrong and 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
  37. S. N. Armstrong and M. Trokhimtchouk. Long-time asymptotics for fully nonlinear homogeneous parabolic equations, Calc. Var. Partial Differential Equations 38 (2010), 521-540. arXiv | journal
  38. S. N. Armstrong. The Dirichlet problem for the Bellman equation at resonance, J. Differential Equations 247 (2009), 931-955. arXiv | journal
  39. S. N. Armstrong. Principal eigenvalues and an anti-maximum principle for homogeneous fully nonlinear elliptic equations, J. Differential Equations 246 (2009), 2958-2987. arXiv | journal
  40. S. N. Armstrong and 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
  41. S. Armstrong, 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