# ERC Regularity and Stability in Partial Differential Equations (RSPDE)

## Papers

### 2018

1. Regularity results for the equation u11u22=1 (by C. Mooney, O. Savin)
2. Singularities of complex-valued solutions to linear parabolic equations (by C. Mooney)
3. On the Singular Set in the Thin Obstacle Problem: Higher Order Blow-ups and the Very Thin Obstacle Problem (by X. Fernández-Real, Y. Jhaveri)
4. On global solutions to semilinear elliptic equations related to the one-phase free boundary problem (by X. Fernández-Real, X. Ros-Oton)
5. Regularity of minimal surfaces with lower dimensional obstacles (by X. Fernández-Real, J. Serra)
6. The Monge-Ampère Equation (by C. Mooney)
7. Strong Sard Conjecture and regularity of singular minimizing geodesics for analytic sub-Riemannian structures in dimension 3
(by A. Belotto da Silva, A. Figalli, A. Parusiński, L. Rifford)
8. Regularity of interfaces in phase transitions via obstacle problems (by A. Figalli)
9. Free boundary regularity in obstacle problems (by A. Figalli)
10. On the Monge-Ampère equation (by A. Figalli)
11. On the Continuity of Center-Outward Distribution and Quantile Functions (by A. Figalli)
12. Singularities of complex-valued solutions to linear parabolic equations (by C. Mooney)

### 2017

1. Quantitative stability of the free boundary in the obstacle problem (by S. Serfaty, J. Serra)
2. Optimal regularity and structure of the free boundary for minimizers in cohesive zone models (by L. Caffarelli, F. Cagnetti, A. Figalli)
3. The Lagrangian structure of the Vlasov-Poisson system in domains with specular reflection (by X. Fernández-Real)
4. On the (In)stability of the Identity Map in Optimal Transportation (by Y. Jhaveri)
5. Partial Regularity of Solutions to the Second Boundary Value Problem for Generated Jacobian Equations (by Y. Jhaveri)
6. Regularity theory for general stable operators: parabolic equations (by X. Fernández-Real, X. Ros-Oton)
7. The obstacle problem for the fractional Laplacian with critical drift (by X. Fernández-Real, X. Ros-Oton)
8. An obstacle problem for conical deformations of thin elastic sheets (by A. Figalli, C. Mooney)
9. Dimension of the minimum set for the real and complex Monge-Ampère equations in critical Sobolev spaces (by T. C. Collins, C. Mooney)
10. Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations (by M. Bonforte, A. Figalli, J.L. Vazquez)
11. On the fine structure of the free boundary for the classical obstacle problem (by A. Figalli, J. Serra)
12. On stable solutions for boundary reactions: a De Giorgi-type result in dimension 4+1 (by A. Figalli, J. Serra)
13. A rigorous derivation from the kinetic Cucker-Smale model to the pressureless Euler system with nonlocal alignment (by A. Figalli, M-J. Kang)
14. Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains (by M. Bonforte, A. Figalli, J.L. Vazquez)
15. Quantitative stability of the free boundary in the obstacle problem (by S. Serfaty, J. Serra)