PREPRINTS AND SOME RECENT PAPERS (.ps or .pdf)

      An Aleksandrov type estimate for alpha convex functions , (with F. Tournier), Proc. AMS, to appear.

      Schauder estimates for sub elliptic equations, (with E. Lanconelli), Journal of Evolution Equations, to appear.

      The refractor problem in reshaping light beams, (with Qingbo Huang), Archive for Rational Mechanics and Analysis, 2009, vol. 193, no 2, pp. 423-443.

      Covering theorems, inequalities on metric spaces and applications to pde's, (with G. Di Fazio and E. Lanconelli), Math. Ann. (2008) 341:255-291.

      On the regularity of reflector antennas, (with L. A. Caffarelli and Qingbo Huang), Annals of Mathematics, 167 (2008), 299-323.

      On Monge-Ampere type equations arising in optimal transportation problems, (with T. Van Nguyen), Calc. Var. (2007) 28: 275-316.

      W2p estimates for the linearized Monge-Ampère equation, (with F. Tournier), Trans. Amer. Math. Soc. 358 (2006) 4843-4872.

      Homogenization and convergence of correctors in Carnot groups, (with B. Franchi and T. Van Nguyen), Comm. Partial Differential Equations, 2005, Vol. 30, Issue 12, 1817-1841.

      On the second order derivatives of convex functions on the Heisenberg group, (with A. Montanari), Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 3 (2004), no. 2, 349--366.

      Maximum and comparison principles for convex functions on the Heisenberg group, (with A. Montanari), Comm. Partial Differential Equations, 2004, Vol. 29, Issue 9/10, 1305-1334.

      Homogenization of Quasilinear Parabolic Equations in Periodic Media, (with J. Garcia--Azorero, and I. Peral), Comm. Partial Differential Equations, 2003, Vol. 28, Issue 11/12, 1887-1910.

      Maximum principle, Harnack inequality, and Liouville theorems for X--elliptic operators, (with E. Lanconelli), Comm. Partial Differential Equations, 2003, Vol. 28, Issue 11/12, 1833-1862.

      Regularity of weak solutions to the Monge-Ampère equation, (with D. Hartenstine), Trans. Amer. Math. Soc. 355 (2003) 2477-2500.

      W2-p-estimates for the parabolic Monge-Ampère equation, (with Q. Huang), Arch. Ration. Mech. Anal. 159 (2001), no. 2, 137--177.

      A Harmonic Analysis theorem and applications to Homogenization, (with I. Peral), Indiana Univ. Math. J. 50 (2001), no. 4, 1651--1674.

     Riesz Transforms, g-functions, and multipliers for the Laguerre semigroup , (with A. Incognito and J. L. Torrea), Houston J. Math. 27 (2001), no. 3, 579--592.

     Geometric Properties of the Sections of  Solutions to the Monge-Ampère  Equation , (with Q. Huang), Transactions of the A. M. S. 352 (2000), no. 9, 4381--4396.  

    A generalization of a theorem by Calabi to the parabolic Monge-Ampère equation, (with Q. Huang), Indiana Univ. Math. Journal 47 (1998), no. 4, 1459--1480.

    Properties of the Solutions of the Linearized Monge-Ampère Equation, (with L. A. Caffarelli), American J. of Math., vol. 119(2), 1997, 423-465.

    Singular Integrals Related to the Monge-Ampère Equation, (with L. A. Caffarelli), in "Wavelet Theory and Harmonic Analysis in Applied Sciences," edited by C. E. D'Attellis and E. M. Fernández-Berdaguer; Birkhauser, 1997, pages 3-13.
 
    Real Analysis Related to the Monge-Ampère Equation, (with L. A. Caffarelli), Transactions of A. M. S., vol. 348(3), 1996, 1075-1092.

    On the Harnack Inequality for Viscosity Solutions of Non-Divergence Equations, Sinet, Ethiopian Journal of Science, Proc. of the conference in Honor of T. Retta, edited by S. Berhanu, vol. 19, 1996, 48-72.