Papers


  1. Homogeneity of blow-up limits for a  free boundary problem with p--Laplace equation, in preparation
  2. Sobolev spaces and uniform estimates in perforated domains, Joint with H.Shahgholian and M.Stromquist, in preparation
  3. Regularity for energy-minimizing area-preserving deformations, preprint, pdf
  4. Holder continuity of viscosity solutions to ut-Δαu=f, preprint, pdf
  5. Existence and Regularity of reflector surfaces in Rn+1, preprint, pdf
  6. Remarks on the regularity of weak solutions for a refractor problem, submitted
  7. Optimal growth estimates for a two phase free boundary problem, submitted, pdf
  8. Regularity of free boundary in continuous casting problem, Joint with J.Rodrigues, preprint, pdf
  9. Analysis of a free boundary at contact point with Lipschitz data, Joint with H.Shahgholian, submitted, pdf
  10. Sufficient conditions for regularity of area-preserving deformations, Manuscripta Math, 138, 463--476, 2012 pdf
  11. The geometry of solutions to a segregation problem for non-divergence systems, Joint with L.A. Caffarelli and Fang-Hua Lin, J. of Fixed Point Theory and Appl.,5 (2009), no. 2, 319--351. pdf
  12. On the reflector shape design, Joint with Xu-Jia Wang, Journal of Diff. Geometry, 84 (2010), no. 3, 561--610, pdf
  13. On the regularity of weak solutions to refractor problem, Arm. J. Math. 2, Issue 1, pp. 28-37, 2009, pdf
  14. On Derivation of Euler-Lagrange Equations for incompressible energy-minimizers, Joint with N.Chaudhuri, Cal. of Variations and PDE,36 (2009), no. 4, 627--645 pdf
  15. Lectures on gas flow in porous media, Joint with L.A. Caffarelli, Appl. Numer. Harmon. Anal., 133--157, Birkhauser Boston, Inc., Boston, MA, 2010, pdf
  16. The reflector design problem, Joint with Xu-Jia Wang, Proceedings of Inter. Congress of Chinese Mathematicians, vol 2, 1-4, 1--24, 2007, pdf
  17. On the Lipschitz regularity of solutions of minimum problem with free boundary, Interfaces and Free Boundaries, 10 (2008), no. 1, 79--86. pdf
  18. The behavior of the free boundary near the fixed boundary for a minimization problem. Joint with C. Kenig and H. Shahgholian, Calc. Var. Partial Differential Equations 28 (2007), no. 1, 15--31. pdf
  19. Up-to boundary regularity for a singular perturbation problem of p--Laplacian type. J. Differential Equations 226 (2006), no. 2, 558--571. pdf
  20. Nonlinear free boundary problems with singular source terms. Joint with A. Hakobyan, A. Monatsh. Math. 142 (2004), no. 1-2, 7-16, pdf