Preprints

  1. S. Armstrong, S. Ferguson and T. Kuusi. Homogenization, linearization and large-scale regularity for nonlinear elliptic equations. arXiv
  2. S. Armstrong, A. Hannukainen, T. Kuusi and J.-C. Mourrat. An iterative method for elliptic problems with rapidly oscillating coefficients. 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 November 22, 2017.)

Articles

  1. S. Armstrong, A. Bordas and J.-C. Mourrat. Quantitative stochastic homogenization and regularity theory of parabolic equations. Anal. & PDE, 11 (2018), 1945-2014. arXiv | journal
  2. S. Armstrong and P. Dario. Elliptic regularity and quantitative homogenization on percolation clusters. Comm. Pure Appl. Math., to appear. arXiv | journal
  3. 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
  4. 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
  5. S. Armstrong, T. Kuusi and J.-C. Mourrat. The additive structure of elliptic homogenization. Invent. Math., 208 (2017), 999-1154. arXiv | journal
  6. S. Armstrong, A. Gloria and T. Kuusi. Bounded correctors in almost periodic homogenization. Arch. Ration. Mech. Anal., 222 (2016), 393-426. arXiv | journal
  7. 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
  8. S. Armstrong and J.-P. Daniel. Calderón-Zygmund estimates for stochastic homogenization. J. Functional Anal., 270 (2016), 312-329. arXiv | journal
  9. S. Armstrong and P. Cardaliaguet. Stochastic homogenization of quasilinear Hamilton-Jacobi equations and geometric motions. J. Eur. Math. Soc., 20 (2018), 797-864. arXiv | journal
  10. 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
  11. 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
  12. S. N. Armstrong and Z. Shen. Lipschitz estimates in almost-periodic homogenization. Comm. Pure Appl. Math., 69 (2016), 1882-1923. arXiv | journal
  13. 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.
  14. S. N. Armstrong and O. Zeitouni. Local asymptotics for controlled martingales. Ann. Appl. Probab., 26 (2016), 1467-1494. arXiv | journal
  15. 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
  16. S. N. Armstrong and P. Cardaliaguet. Quantitative stochastic homogenization of viscous Hamilton-Jacobi equations, Comm. PDE, 40 (2015), 540-600. arXiv | journal
  17. 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
  18. S. N. Armstrong and H. V. Tran. Viscosity solutions of general viscous Hamilton-Jacobi equations, Math. Ann., 361 (2015), 647-687. arXiv | journal
  19. 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
  20. 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
  21. 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
  22. 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
  23. 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
  24. 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
  25. 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
  26. S. N. Armstrong and P. E. Souganidis. Stochastic homogenization of $L^\infty$ variational problems, Adv. Math., 229 (2012), no. 6, 3508-3535. arXiv | journal
  27. 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
  28. 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
  29. 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
  30. S. N. Armstrong and L. Silvestre. Unique continuation for fully nonlinear elliptic equations, Math. Res. Lett., 18 (2011), no. 5, 921-926. arXiv | journal
  31. 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
  32. 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
  33. 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
  34. 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
  35. 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
  36. 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
  37. 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
  38. 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
  39. S. N. Armstrong. The Dirichlet problem for the Bellman equation at resonance, J. Differential Equations 247 (2009), 931-955. arXiv | journal
  40. 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
  41. 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
  42. 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