# Free boundary problems

### Published/accepted papers

- Generic regularity of free boundaries for the obstacle problem (with X. Ros-Oton and J. Serra)

*Publ. Math. Inst. Hautes Études Sci.*, to appear
- On the obstacle problem for the 1D wave equation (with X. Fernández-Real)

*Math. Eng.* 2 (2020), no. 4, 584-597.
- Optimal regularity and structure of the free boundary for minimizers in cohesive zone models (with L. Caffarelli and F. Cagnetti)

*Arch. Ration. Mech. Anal.* 237 (2020), no. 1, 299–345.
- On the fine structure of the free boundary for the classical obstacle problem (with J. Serra)

*Invent. Math.*, 215 (2019), no. 1, 311-366.
- Free boundary regularity in the parabolic fractional obstacle problem (with B. Barrios and X. Ros-Oton)

*Comm. Pure Appl. Math.* 71 (2018), no. 10, 2129-2159.
- Global regularity for the free boundary in the obstacle problem for the fractional Laplacian (with B. Barrios and X. Ros-Oton)

*Amer. J. Math.* 140 (2018), no. 2, 415-447.
- On the regularity of the free boundary in the p-Laplacian obstacle problem (with B. Krummel and X. Ros-Oton)

*J. Differential Equations*, 263 (2017), no. 3, 1931-1945.
- A note on the dimension of the singular set in free interface problems (with G. De Philippis)

*Differential Integral Equations* 28 (2015), 523-536.
- A general class of free boundary problems for fully nonlinear parabolic equations (with H. Shahgholian)

*Ann. Mat. Pura Appl. (4)* 194 (2015), no. 4, 1123-1134.
- Higher integrability for minimizers of the Mumford-Shah functional (with G. De Philippis)

*Arch. Ration. Mech. Anal.* 213 (2014), no. 2, 491-502.
- A general class of free boundary problems for fully nonlinear elliptic equations (with H. Shahgholian)

*Arch. Ration. Mech. Anal.* 213 (2014), no. 1, 269-286.
- Regularity of solutions to the parabolic fractional obstacle problem (with L. Caffarelli)

*J. Reine Angew. Math.* 680 (2013), 191-233.

### Submitted papers

- The singular set in the Stefan problem (with X. Ros-Oton and J. Serra)
- Lipschitz Regularity in Vectorial Linear Transmission Problems (with S. Kim and H. Shahgholian)

### Lecture notes and reviews

- Regularity of interfaces in phase transitions via obstacle problems

Proceedings of the International Congress of Mathematicians, 2018.

Vol. I. Plenary lectures, 225–247, *World Sci. Publ.,* Hackensack, NJ, 2018.
- Free boundary regularity in obstacle problems

*Journées EDP 2018*, to appear.
- An overview of unconstrained free boundary problems (with H. Shahgholian)

*Philos. Trans. A* 373 (2015), no. 2050, 20140281, 11 pp.