Homogenization: Equations in divergence form

  1. S. Armstrong, A. Bordas and J.-C. Mourrat. Quantitative stochastic homogenization and regularity theory of parabolic equations. arXiv
  2. S. Armstrong, T. Kuusi and J.-C. Mourrat. Quantitative stochastic homogenization and large-scale regularity. arXiv | pdf
  3. S. Armstrong and P. Dario. Elliptic regularity and quantitative homogenization on percolation clusters. Comm. Pure Appl. Math., to appear. arXiv
  4. S. Armstrong, T. Kuusi, J.-C. Mourrat and C. Prange. Quantitative analysis of boundary layers in periodic homogenization. Arch. Ration. Mech. Anal., to appear. 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. 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 and Z. Shen. Lipschitz estimates in almost-periodic homogenization. Comm. Pure Appl. Math., 69 (2016), 1882-1923. arXiv | journal
  11. 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

Homogenization: Equations in nondivergence form

    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
  1. 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
  2. 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
  3. 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

Homogenization: Hamilton-Jacobi equations

  1. S. Armstrong and P. Cardaliaguet. Stochastic homogenization of quasilinear Hamilton-Jacobi equations and geometric motions. J. Eur. Math. Soc., to appear. arXiv
  2. 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
  3. 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
  4. S. N. Armstrong and P. Cardaliaguet. Quantitative stochastic homogenization of viscous Hamilton-Jacobi equations, Comm. PDE, 40 (2015), 540-600. arXiv | journal
  5. S. N. Armstrong and H. V. Tran. Viscosity solutions of general viscous Hamilton-Jacobi equations, Math. Ann., 361 (2015), 647-687. arXiv | journal
  6. 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
  7. 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
  8. 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
  9. S. N. Armstrong and P. E. Souganidis. Stochastic homogenization of $L^\infty$ variational problems, Adv. Math., 229 (2012), no. 6, 3508-3535. arXiv | journal
  10. 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

Fully nonlinear elliptic equations

  1. 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
  2. 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
  3. S. N. Armstrong and L. Silvestre. Unique continuation for fully nonlinear elliptic equations, Math. Res. Lett., 18 (2011), no. 5, 921-926. arXiv | journal
  4. 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
  5. 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
  6. 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
  7. S. N. Armstrong. The Dirichlet problem for the Bellman equation at resonance, J. Differential Equations 247 (2009), 931-955. arXiv | journal
  8. 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

Infinity Laplacian

  1. 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
  2. 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
  3. 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
  4. 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

Miscellaneous

  • S. N. Armstrong and O. Zeitouni. Local asymptotics for controlled martingales. Ann. Appl. Probab., 26 (2016), 1467-1494. arXiv | journal
  • S. N. Armstrong and H. V. Tran. Viscosity solutions of general viscous Hamilton-Jacobi equations, Math. Ann., 361 (2015), 647-687. arXiv | journal
  • 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
  • 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
  • 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
  • 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