# Daniela De Silva

## Associate Professor of Mathematics

Daniela De Silva, associate professor of mathematics, joined the faculty of Barnard in 2007. Formerly, she was a member of the Mathematical Sciences Research Institute in Berkeley. Professor De Silva has also taught at John Hopkins, MIT, and the University of Naples "Federico II". At Barnard, her teaching duties include Calculus and Analysis.

Professor De Silva's primary research area is partial differential equations. She is particularly interested in the regularity theory for free boundary/phase transition problems.

Professor De Silva is the organizer of the Geometry and Analysis seminar at Columbia University.

**Selected Publications**

"Gradient bound for energy minimizing free boundary graphs", (with D. Jerison), *Comm. on Pure and Applied Math.*, Volume 64, Issue 4 (2011), 538–555.

"Minimizers of convex functionals arising in random surfaces," (with O. Savin), *Duke Math. J.,* Volume 151, Number 3 (2010), 487-532.

"Rearrangements and Radial Graphs of Constant Mean Curvature in Hyperbolic Space" (with J. Spruck), *Calculus of Variations and PDEs, * 34 no. 1, 73--95.

"A Singular Energy Minimizing Free Boundary" (with D. Jerison), * J. Reine Angew. Math.,* Vol. 2009 Issue 635, 1--22.

"Existence and Regularity of Monotone Solutions to a Free Boundary Problem,"*Amer. J. of Math.*, 131, no. 2, 351--378.

"Bernstein-Type Techniques for 2D Free Boundary Graphs," *Math.Z.*, 260, no. 1, 47--60.

"Symmetry of Global Solutions to a Class of Fully Nonlinear Elliptic Equations in 2D" (with O. Savin), *Indiana Univ. Math. J.*, 2009; 58 (1), 301--315.

"Global Well-Posedness and Polynomial Bounds for the Defocusing L2-Critical Nonlinear Schrödinger Equation in R" (with N. Pavlovic, G. Staffilani and N. Tzirakis), *Comm. in PDEs*, Vol. 33 (2008), n. 8, 1395--1429(35).

"Low Regularity Solutions for a 2D Quadratic Non-Linear Schrödinger Equation" (with I. Bejenaru), *Trans. of AMS*, 360 (2008), 5805-5830.

"Global Well-Posedness for a Periodic Nonlinear Schrödinger Equation in 1D and 2D" (with N. Pavlovic, G. Staffilani and N. Tzirakis), *Discrete Contin. Dyn. **Syst.*19 (2007)

"Global Well-Posedness for the L2 Critical Nonlinear Schrödinger Equation in Higher Dimensions" (with N. Pavlovic, G. Staffilani and N. Tzirakis), *Commun. Pure Appl. Anal.* 6 (2007)

"Some Remarks on Nonlinear Elliptic Equations and Applications to Hamilton-Jacobi Equations" (with C. Trombetti), *C.R. Acad. Sci. Paris*, t. 333, Serie I, (2001)

Partial differential equations

Harmonic analysis

212.854.5135

desilva@math.columbia.edu

B.A., University of Naples Federico II

Ph.D., Massachusetts Institute of Technology