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

## Papers

### 2018

- Regularity results for the equation u11u22=1 (by C. Mooney, O. Savin)
- Singularities of complex-valued solutions to linear parabolic equations (by C. Mooney)
- 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)
- On global solutions to semilinear elliptic equations related to the one-phase free boundary problem (by X. Fernández-Real, X. Ros-Oton)
- Regularity of minimal surfaces with lower dimensional obstacles (by X. Fernández-Real, J. Serra)
- The Monge-Ampère Equation (by C. Mooney)
- 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) - Regularity of interfaces in phase transitions via obstacle problems (by A. Figalli)
- Free boundary regularity in obstacle problems (by A. Figalli)
- On the Monge-Ampère equation (by A. Figalli)
- On the Continuity of Center-Outward Distribution and Quantile Functions (by A. Figalli)
- Singularities of complex-valued solutions to linear parabolic equations (by C. Mooney)

### 2017

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