About me
I am currently SNF Ambizione Fellow at ETH.
My research is on elliptic and parabolic Partial Differential Equations.
More precisely:
- Stable interfaces (phase transitions and minimal surfaces)
- Free boundaries (the singular sets in the obstacle problem and the Stefan problem)
- Elliptic and parabolic integro-differential equations (integration by part type identities with singular boundary terms, regularity for fully nonlinear equations)
- Reaction-diffusion equations, isoperimetric problems
Selected papers from the last 5 years (all of my papers are available at arXiv; see also the Publications and Preprints page for direct links to pdf).
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A. Figalli, X. Ros-Oton, J. Serra,
Generic regularity of free boundaries for the obstacle problem,
Publ. Math. IHÉS, to appear. -
X. Cabré, A. Figalli, X. Ros-Oton, J. Serra,
Stable solutions to semilinear elliptic equations are smooth up to dimension 9,
Acta Math., 224 (2020), 187-252. -
A. Figalli, J. Serra,
On the fine structure of the free boundary for the classical obstacle problem,
Invent. Math. 215 (2019), 311–366. -
A. Figalli, J. Serra,
On stable solutions for boundary reactions: a De Giorgi type result in dimension 4+1,
Invent. Math. 219 (2020), 153–177. -
S. di Pierro, J. Serra, E. Valdinoci,
Improvement of flatness for nonlocal phase transitions,
Amer. J. Math, to appear. -
E. Cinti, J. Serra, E. Valdinoci,
Quantitative flatness results and BV-estimates for nonlocal minimal surfaces,
J. Differential Geom. 112 (2019), 447-504. -
L. Caffarelli, X. Ros-Oton, J. Serra,
Obstacle problems for integro-differential operators: regularity of solutions and free boundaries,
Invent. Math. 208 (2017), 1155-1211. - X. Ros-Oton, J. Serra,
Boundary regularity for fully nonlinear integro- differential equations,
Duke Math. J. 165 (2016), 2079-2154.