Research

Papers:

De Silva D. Savin O., Boundary Harnack estimates in slit domains and applications to thin free boundary problems. Submitted.
De Silva D., Ferrari F., Salsa S., Perron's solutions for two-phase free boundary problems with distributed sources. Submitted.
De Silva D. Savin O., Sire Y., A One-Phase Problem For The Fractional Laplacian: Regularity Of Flat Free Boundaries. Bulletin of the Institute of Mathematics Academia Sinica New Series.
De Silva D., Ferrari F., Salsa S., On two phase free boundary problems governed by elliptic equations with distributed sources. Discrete and Continuous Dynamical Systems, DCDS.
De Silva D., Ferrari F., Salsa S., Regularity of the free boundary in problems with distributed sources. Geometric Methods in PDE's.
De Silva D., Savin O., $C^\infty$ regularity of certain thin free boundaries. Submitted.
De Silva D., Savin O., A note on higher regularity boundary Harnack inequality. Discrete and Continuous Dynamical Systems, DCDS-A. .
De Silva D., Ferrari F., Salsa S., Free boundary regularity for fully nonlinear non-homogeneous two-phase problems . arXiv:1304.0406. To appear in Journal de Mathematiques Pures et Appliquees.
De Silva D., Savin O., Regularity of Lipschitz free boundaries for the thin one-phase problem. arXiv:1205.1755. To appear in Journal of the European Mathematical Society.
De Silva D., Ferrari F., Salsa S., Two-phase problems with distributed source: regularity of the free boundary. arXiv:1210.7226. To appear in Analysis and PDE.
De Silva D., Savin O., $C^{2,\alpha}$ regularity of flat free boundaries for the thin one- phase problem, J. Differential Equations 253 (2012), no. 8, 2420-2459.
De Silva D., Roquejoffre J.M., Regularity in a one-phase free boundary problem for the fractional Laplace, Ann. Inst. H. Poincare Anal. Non Lineaire 29 (2012), no. 3, 335-367.
De Silva D., Free boundary regularity for a problem with right hand side, Interfaces and free boundaries 13 (2011), 223-238.
De Silva D., Jerison D., Gradient bound for energy minimizing free boundary graphs, Comm. on Pure and Applied Math. Volume 64, Issue 4 (2011), 538-555.
De Silva D., Valdinoci E., A fully nonlinear problem with free boundary in the plane, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. IX (2010), 111-132.
De Silva D., Savin O., Minimizers of convex functionals arising in random surfaces, Duke Math. J., Volume 151, Number 3 (2010), 487-532.
De Silva D., Spruck J., Radial graphs of constant mean curvature in the Hyperbolic space, Calculus of Variations and PDEs 34 (2009), no. 1, 73-95.
De Silva D., Bernstein-type techniques for 2D free boundary graphs, Math. Z. 260 (2008), no. 1, 47-60.
De Silva D., Savin O., Symmetry of global solutions to a class of fully nonlinear elliptic equations in 2D, Indiana Univ. Math. J., 2009; 58 (1), 301-315.
De Silva D., Jerison D., A singular energy minimizing free boundary, J. Reine Angew. Math., Vol. 2009 Issue 635, 1-22.

Supporting files:

Subsolution property [.nb]
Strict subsolution property [.nb]
Supersolution properties [.nb]

De Silva D., Existence and regularity of monotone solutions to free boundary problems, Amer. J. of Math. 131 (2009), no. 2, 351-378.
Bejenaru I., De Silva D., Low regularity solutions for a 2D quadratic non-linear Schrodinger equation, Trans. Amer. Math. Soc. 360 (2008), 5805-5830.
De Silva D., Pavlovic N., Staffilani G., Tzirakis N., Global well-posedness and polynomial bounds for the defocusing L2-critical nonlinear Schro?odinger equation in R, Comm. in PDEs. Vol. 33 (2008), n. 8, 1395-1429(35).
De Silva D., Pavlovic N., Staffilani G., Tzirakis N., Global well-Posedness for the L2-critical nonlinear Schrodinger equation in higher dimensions, CPAA, Vol. 6 (2007), n.4, 1023-1041.
De Silva D., Pavlovic N., Staffilani G., Tzirakis N.,Global well-posedness for a periodic nonlinear Schrodinger equation in 1D and 2D , Discrete and Continuous Dynamical Systems, Vol. 19 (2007), n. 1, 37-65.
De Silva D., Estimates for the gradient of solutions of elliptic equations in Orlicz- Sobolev spaces, Ricerche di Matematica, vol. LI, issue 1, p. 25-47, 2002
De Silva D., Trombetti C., Some remarks on nonlinear elliptic equations and applications to Hamilton-Jacobi equations, C.R. Acad. Sci. Paris, t. 333, Serie I, p. 91-96, 2001.