- Lecture notes on elliptic equations, pdf

- New trends in free boundary problems, Joint with
S. Dipierro and E. Valdinoci, submitted, pdf

- Remarks on the thin obstacle problem and constrained Ginibre ensembles, submitted, pdf

- Classification of irregular free boundary points for non-divergence type
equations with discontinuous coefficients, Joint with
S. Dipierro and E. Valdinoci, submitted, pdf

- A geometric approach to regularity for nonlinear free boundary problems, submitted, pdf

- A nonlinear free boundary problem with a self-driven Bernoulli condition, Joint with
S. Dipierro and E. Valdinoci, submitted, pdf

- Embedded $K$-surfaces with free boundaries, Joint with H. Aleksanyan

- Capillary surfaces arising in singular perturbation problems, pdf

- A class of unstable free boundary problems, Joint with
S. Dipierro and E. Valdinoci, submitted, pdf

- Blaschke's rolling ball theorem and the Trudinger-Wang monotone bending, Journal of Differential Equations, in press, pdf
- Boundary behavior for a singular perturbation problem,
Joint with H.Shahgholian,
Nonlinear Analysis Series A, TMA, in press, pdf

- A new discrete monotonicity formula with application
to a two-phase free boundary problem in dimension two, Joint with S.
Dipierro, pdf

- Stratification of free boundary points for a two-phase
variational problem, Joint with S. Dipierro, pdf

- Estimates for capacity and discrepancy of convex surfaces in sieve-like domains with an application to homogenization, Joint with M.Stromqvist, Cal. of Variations and PDE, in press, pdf
- Regularity for a quasilinear continuous casting problem, submitted, pdf
- Potential theoretic approach to Schauder estimates for the fractional Laplacian, Joint with C. Bucur, Proceedings of the AMS, in press, pdf
- On a conjecture of De Giorgi related to
homogenization, Joint with H.Shahgholian,
submitted, pdf

- Lipschitz continuity of free boundary in the continuous casting problem with divergence form elliptic equation, Discrete and Cont. Dynamical Systems, 36 (2016), no. 1, 261--277 pdf
- Regularity for energy-minimizing area-preserving deformations, Journal of Elasticity, Volume 114, Issue 2 (2014), pp 213−223, pdf
- Application of uniform distribution to homogenization of a thin obstacle problem with $p$-Laplacian, Joint with M.Stromqvist, Communications in PDEs, 39 (2014), no. 10 1870--1897, pdf
- An inverse problem for the refractive surfaces with parallel lighting, SIAM Journal of Mathematical Analysis, in press, pdf
- Existence and regularity of the reflector surfaces in $\mathbb R^{n+1}$, Archive for Rational Mechanics and Analysis, 213 (2014), no. 3, 833--885, pdf
- Optimal Regularity for phase transition problems with convection, Annales de l'Institut Henri Poincare, Analyse non lineaire, 32 (2015), no. 4, 715--740, pdf
- The Stefan problem with constant convection, Joint with J.Rodrigues, preprint, pdf
- Analysis of a free boundary at contact point with Lipschitz data, Joint with H.Shahgholian, Transactions of the AMS, 367 (2015), no. 7, 5141--5175, pdf
- Sufficient conditions for regularity of area-preserving deformations, Manuscripta Math, 138, 463--476, 2012, pdf
- 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
- On the reflector shape design, Joint with Xu-Jia Wang, Journal of Differential Geometry, 84 (2010), no. 3, 561--610, pdf
- On the regularity of weak solutions to refractor problem, Arm. J. Math. 2, Issue 1, pp. 28-37, 2009, pdf
- 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
- 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
- The reflector design problem, Joint with Xu-Jia Wang, Proceedings of Inter. Congress of Chinese Mathematicians, vol 2, 1-4, 1--24, 2007, pdf
- On the Lipschitz regularity of solutions of minimum problem with free boundary, Interfaces and Free Boundaries, 10 (2008), no. 1, 79--86, pdf
- 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
- Up-to boundary regularity for a singular perturbation problem of $p$-Laplacian type. J. Differential Equations 226 (2006), no. 2, 558--571, pdf
- Nonlinear free boundary problems with singular source terms. Joint with A. Hakobyan, Monatsh. Math. 142 (2004), no. 1-2, 7-16, pdf