PUBLICATIONS

A rate of convergence for monotone finite difference approximations to fully nonlinear uniformly elliptic PDE (with Luis Caffarelli), Comm. Pure Applied Math., accepted.
Dissipative and entropy solutions to non-isotopic degenerate parabolic balance laws (with B. Perthame), Arch. Rat. Mech. Anal., in press.
Homogenization of degenerate second-order PDE in periodic and almost periodic environments and applications (with P.-L. Lions), Analyse Nonlineaire IHP, to appear.
Large time behavior for viscous and non-viscous Hamilton-Jacobi equations forced by additive noise
Front propagation for a jump process model arising in spatial ecology (with B. Perthame), preprint.
Homogenization of "viscous" Hamilton-Jacobi equations in stationary ergodic media (with P.-L. Lions), Comm. in Partial Dif. Equations, to appear.
Homogenization of Fully Nonlinear, Uniformly Elliptic and Parabolic Partial Differential Equations in Stationary Ergodic Media (with L. Caffarelli and L. Wang), Comm. in Pure Applied Math., to appear.
  • Uniqueness of motion by mean curvature perturbed by stochastic noise (with N. Yip), Analyse Nonlineaire IHP 21 (2004) 1-23.
  • Dissipative and entropy solutions to non-isotropic degenerate parabolic balance laws (with B. Perthame), Arch. Rat. Mech. Anal. 170 (2003) 359-370.
  • Correctors for the homogenization theory of Hamilton-Jacobi equations (with P.-L. Lions), Comm Pure Applied Math. LVI (2003) 1501-1524.
  • Recent developments in the theory of front propagation and its applications, Modern Methods in Scientific Computing and Applications (G. Sabidussi, editor), NATO Science Ser. II 75 (2002) Kluwer.
  • Space-time periodic solutions and long-time behavior of solutions to quasilinear parabolic equations (with G. Barles), SIAM J. Math. Anal. 32 (2001) 1311-1323.
  • Some counterexamples on the asymptotic behavior of the solutions of Hamilton-Jacobi equations (with G. Barles), C.R. Acad. Sci. Paris 330, Serie I (2000) 963-968.
  • Fully nonlinear stochastic partial differential equations with semilinear stochastic dependence (with P.-L. Lions), C. R. Acad. Paris 331, Serie I (2000) 617-624.
  • Uniqueness of weak solutions for fully nonlinear stochastic partial differential equations (with P.-L. Lions), C. R. Acad. Paris 331, Serie I (2000) 783-790.
  • On the large time behavior of solutions Hamilton-Jacobi equations (with G. Barles), SIAM J. Math Anal. 31 (2000) 925-939.
  • The effect of turbulence on mixing in prototype reaction diffusion systems (with A. Majda), Comm. Pure Applied Math LIII (2000) 1284-1304.
  • Stochastic homegenization for Hamilton-Jacobi equations and applications, Asympt. Anal. 20 (1999) 1-11.
  • Finite volume schemes for Hamilton-Jacobi equations (with G. Kossioris and Ch. Makridakis), Numer. Math 83 (1999) 427--442.
  • A limiting case for the averaging lemma motivated by the kinetic formulation of some classical systems in fluid meachanics (with B. Perthame), Dynamical systems, plasma and gravitation, Lect. Notes in Physics 518 (1999) 56-61, Springer Verlag.
  • Fully nonlinear stochastic partial differential equations: Nonsmooth equations and applications (with P.-L. Lions), C. R. Acad. Sci. Paris, 327, Serie I (1998) 735-741.
  • Flame fronts in turbulent combustion models with fractal velocity fields (with A. J. Majda), Comm. Pure Applied Math LI (1998) 1337-1348.
  • Un cas limite des lemmes de compacite en moyenne motive par la formulation cinetique de systemes hyperbolique (with B. Perthame), Journees "Equations aux Derivees Partielles" (Saint Jean - de -Monts) (1997).
  • Remarks on the Dirichlet problem for quasilinear elliptic and parabolic equations (with G. Barles and E. Rouy), Optimization and Applications: A Volume in Honor of W.H. Fleming, W.M. McEneaney, G. Yin, and Q. Zhang (Eds.), Systems and Control: Foundations and Applications series, Birkhauser, Boston, 1998.
  • A limiting case for velocity averaging (with B. Perthame), Ann. Scient. Ec. Norm. Sup. 31 (1998) 591-598.
  • Viscosity solutions of fully nonlinear stochastic partial differential equations (with P.-L. Lions), C.R. Acad. Sci. Paris, 326, Serie I (1998) 1085-1092.
  • Two player, zero sum differential games and viscosity solutions, Stochastic and Differential Games: Theory and Numerical Methods (M. Bardi, T. E. S. Raghavan, T. Parthasarathy, editors), 69-104, Birkhauser (1999).
  • Threshold dynamics type approximation schemes for propagating fronts (with H. Ishii and G. Pires), J. Math. Soc. Japan 51 (1999) 267-308.
  • Examples and counterexamples for Huygens principle in premixed combustion (with P. Embid and A. Majda), Combust. Sci. Tech. 120 (1996) 273-303.
  • A new approach to generalized front propagation problems: Theory and applications (with G. Barles), Arch. Rat. Mech. Anal. 141 (1998) 237-296.
  • Stochastic Ising models and anisotropic front propagation (with M. Katsoulakis), J. Stat. Phys. 87 (1997) 63-89.
  • Front propagation: Theory and Applications, CIME course on viscosity solutions and their applications, Springer-Verlag Lecture Notes Math. 1660, Springer (1997).
  • Bounds on enhanced turbulent flame speeds for combustion with fractal velocity fields (with A. Majda), J. Stat. Phys. 83 (1996) 933-954.
  • Interface dynamics in phase transitions, Proceedings of ICM 94, Birkhauser (1995), 1133-1144.
  • Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates (with P.-L. Lions and B. Perthame), Comm. Pure Applied Math. XLIX (1996) 599-638.
  • Front propagation for reaction-diffusion arising in combustion theory (with G. Barles and C. Georgelin), Asympt. Anal. 14 (1997) 277-292.
  • Comparison of turbulent flame speeds from complete averaging and the G-equation (with P. Embid and A. Majda), Phys. of Fluids 7 (1995) 2052-2060.
  • Effective geometric front dynamics for premixed turbulent combustion with separated velocity scales (with P. Embid and A. Majda), Comb. Sci. Tech. 103 (1995) 85-115.
  • Stability results about entropy solutions of the isentropic gas dynamics system for $\gamma =5/3$ (with P. -L. Lions and B. Perthame), in Progress in elliptic and parabolic differential equation, Pitman Res. Notes Math. Ser 350 (1994) 184-192.
  • Generalized motion by mean curvature as a macroscopic limit for stochastic Ising models with long range interactions and Glauber dynamics (with M. Katsoulakis), Comm. Math. Physics 169 (1995) 61-97.
  • Phase field theory for a Fitz-Hu Nagumo type system (with P. Soravia), SIAM J. Math. Anal. 42 (1996) 1341-1359.
  • Generalized motion of noncompact hypersurfaces with velocity having arbitrary growth on the curvature tensors (with H. Ishii), Tohuko Math. J. 47 (1995) 227--250.
  • Convergence of MUSCL and filtered schemes for scalar conservation laws and Hamilton-Jacobi (with P.-L. Lions), Numerische Math. 69 (1995) 441-470.
  • Anisotropic motion of an interface relaxed by the formation of infinitesimal wrinkles (with M. Gurtin and H.M. Soner), J. Diff. Eqns. 119 (1995) 193-204.
  • A remark on the asymptotic behavior of the solution of the KPP equation (with G. Barles), C.R. Acad. Sci. Paris, S\'erie I 319 (1994) 679-684.
  • Large scale front dynamics for turbulent reaction-diffusion equations with separated velocity scales (with A. Majda), Nonlinearity 7 (1994) 1-30.
  • Interacting particle systems and generalized evolution of fronts (with M. Katsoulakis), Arch. Rat. Mech. Anal. 127 (1994) 133-157.
  • Regularity of solutions of fully nonlinear first-and-second-order pde's with large zeroth order term (with P.-L. Lions), Indiana U. Math. J. 42 (1993) 1525-1543.
  • Front propagation and phase field theory (with G. Barles and H.M. Soner), SIAM J. Control and Optimization 31 (1993) 439-469.
  • Uniqueness and singularities of rotationally symmetric domains moving by mean curvature (with H.M. Soner), Comm. in PDE 18 (1993) 859-894.
  • Phase Transitions and Generalized Motion by Mean Curvature (with L.C. Evans and H.M. Soner), Comm. Pure Applied Math. XLV (1992) 1097-1123.
  • Front propagation for reaction-diffusion equations of bistable type (with L. Bronsard and G. Barles), Anal. Inst. H. Poincare, Analyse Nonlineaire 9 (1992) 479-496.
  • Convergence of MUSCL type methods for scalar conservation laws (with P.-L. Lions), C.R.A.S. 311 S\'erie I (1990) 259-264.
  • Convergence of approximation schemes for fully nonlinear second order equations (with G. Barles), J. Asympt. Anal. 4 (1991) 271-283.
  • Instability of a class of dispersive solitary waves (with W.A. Strauss), Proc. Royal Society, Edinburgh 114A (1990) 195-212.
  • Wave front propagation for reaction-diffusion systems of PDE's (with G. Barles and L.C. Evans), Duke U. Math. J. 61 (1990) 835-859.
  • Difference schemes for quasi-nonlinear evolution equations (with M.G. Crandall), J. Nonl. Analysis: Theory, Methods, Applications 13 (1989) 1375-1392.
  • A PDE approach to certain large deviations problem for systems of parabolic equations (with L.C. Evans), Anal. Non Lineaire, Contributions en l'honneur de J.J. Moreau, Gauthier-Villars, Paris 1989.
  • A PDE approach to geometric optics for certain reaction-diffusion equations (with L.C. Evans), Indiana U. Math. J. 38 (1989) 141-172.
  • On the existence of value functions of two player, zero-sum stochastic differential games (with W.H. Fleming), Indiana U. Math. J. 38 (1989) 293-314.
  • Maximal solutions and universal bounds for some partial differential equations of evolution (with M.G. Crandall and P.-L. Lions), Arch. Rat. Mech. Anal. 105 (1989) 163-190.
  • Two player, zero-sum stochastic differential games, (with W.H. Fleming), in Analyse Mathematique et Applications, Contributions en l'honneur J.L. Lions, Gauthier-Villars, Paris 1988.
  • A uniqueness result for viscosity solutions of second-order fully nonlinear partial differential equations (with R. Jensen and P.-L. Lions), Proc. AMS 102 (1988) 975-978.
  • Viscosity solutions of second-order equations, stochastic control and stochastic differential games, (with P.-L. Lions), in Stochastic Differential Systems, Stochastic Control Theory and Applications, (W.H. Fleming and P.-L. Lions eds.), IMA volumes in Math. and Appl. No. 10, Springer-Verlag, New York 1987.
  • The relation between the porous-medium and eikonal equations in several space dimensions (with P.-L. Lions and J.L. Vazquez), Rev. Mat. Iberoamericana 3 (1987) 275-310.
  • Stability and instability of solitary waves of Korteweg-deVries type (with J.L. Bona and W.A. Strauss), Proc. R. Soc. Lond. A 411 (1987) 395-412.
  • Asymptotic series on the method of vanishing viscosity (with W.H. Fleming), Indiana U. Math. J. 35 (1986) 425-448.
  • Blow-up of solutions of Hamilton-Jacobi equations (with A. Friedman), Comm. PDE 11 (1986) 397-443.
  • A regularity result for viscosity solutions of Hamilton-Jacobi equations in one space dimension (with R. Jensen), Trans. AMS 301 (1987) 137-147.
  • Recent developments in the theory of Hamilton-Jacobi equations, in Dynamics of Infinite Dimensional Systems, (S.N. Chow and J.K. Hale eds.), NATO ASI Series, Springer-Verlag, New York 1987.
  • A remark about viscosity solutions on the boundary, Proc. AMS 96 (1986) 323-330.
  • Differential games, optimal control and directional derivatives of viscosity solutions of Bellman's and Isaacs' equations, II (with P.-L. Lions), SIAM J. Control and Optimization 24 (1986) 1086-1089.
  • PDE-viscosity solution approach to some problems of large deviations (with W.H. Fleming), Ann. di Scuola Norm. Sup., Serie IV, 13 (1986) 171-192.
  • Differential games, optimal control and directional derivatives of viscosity solutions of Bellman's and Isaacs' equations (with P.-L. Lions), SIAM J. Control and Optimization 23 (1985) 566-583.
  • Convergence of difference approximations of quasilinear evolution equations (with M.G. Crandall), J. Nonlinear Anal.: Theory, Methods, Applications 10 (1986) 425-446.
  • Asymptotic series for solutions to the dynamic programming equation for diffusions with small noise (with W.H. Fleming), in Proceeding of 24th IEEE Conference on Decision and Control, December 1985.
  • Max-min representations and product formulas for viscosity solutions of Hamilton-Jacobi equations with applications to differential games, J. Nonlinear Anal.: Theory, Methods, Applications 9 (1985) 217-257.
  • Approximation schemes for viscosity solutions of Hamilton-Jacobi equations, J. Diff. Eqns. 59 (1985) 1-43.
  • Existence of viscosity solutions of Hamilton-Jacobi equations, J. Diff. Eqns. 56 (1985) 345-390.
  • A PDE approach to some large deviations problems (with W.H. Fleming), in Nonlinear systems of PDE in Applied Mathematics, AMS Lectures in Applied Mathematics 23, AMS-SIAM Summer Seminar 1984.
  • Developments in the theory of nonlinear first-order partial differential equations (with M.G. Crandall), in Proceedings of International Conference on Differential Equations, Birmingham, Alabama, 1983 (Knowles and Lewis, Eds), North-Holland Math. Studies 92, North-Holland, Amsterdam, 1984.
  • Differential games and representation formulas for solutions of Hamilton-Jacobi-Isaacs equations (with L.C. Evans), Indiana U. Math. J. 33 (1984) 773-797.