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ERC Regularity and Stability in Partial Differential Equations (RSPDE)



  1. Duality of capacities and Sobolev extendability in the plane (by Y. Zhang)


  1. Sharp Extinction Rates for Fast Diffusion Equations on Generic Bounded Domains (by M. Bonforte, A. Figalli)
  2. Regularity of monotone transport maps between unbounded domains (by D. Cordero-Erausquin, A. Figalli)
  3. On the sharp stability of critical points of the Sobolev inequality (by A. Figalli, F. Glaudo)
  4. Symmetry results for critical anisotropic p-Laplacian equations in convex cones (by G. Ciraolo, A. Figalli, A. Roncoroni)
  5. Stable solutions to semilinear elliptic equations are smooth up to dimension 9 (by X. Cabré, A. Figalli, X. Ros-Oton, J. Serra)
  6. Strong stability for the Wulff inequality with a crystalline norm (by A. Figalli, Y. Zhang)
  7. Generic regularity of free boundaries for the obstacle problem (by A. Figalli, X. Ros-Oton, J. Serra)
  8. On the obstacle problem for the 1D wave equation (by X. Fernández-Real, A. Figalli)
  9. 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)
  10. Regularity of minimal surfaces with lower dimensional obstacles (by X. Fernández-Real, J. Serra)
  11. Free boundary regularity for almost every solution to the Signorini problem (by X. Fernández-Real, X. Ros-Oton)
  12. Ahlfors reflection theorem for p-morphisms (by P. Koskela, P. Pankka, Y. Zhang)
  13. Singular solutions and a critical Yamabe problem revisited (by H. Chan, A. DelaTorre)
  14. ODE-methods in non-local equations (by W. Ao, H. Chan, A. DelaTorre, M. A. Fontelos, M. Del Mar González, J. Wei)
  15. On the optimal map in the 2-dimensional random matching problem (by L. Ambrosio, F. Glaudo, D. Trevisan)
  16. Finer estimates on the 2-dimensional matching problem (by L. Ambrosio, F. Glaudo, D. Trevisan)


  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 global solutions to semilinear elliptic equations related to the one-phase free boundary problem (by X. Fernández-Real, X. Ros-Oton)
  4. The Monge-Ampère Equation (by C. Mooney)
  5. 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)
  6. Free boundary regularity in obstacle problems (by A. Figalli)
  7. On the Monge-Ampère equation (by A. Figalli)
  8. On the Continuity of Center-Outward Distribution and Quantile Functions (by A. Figalli)
  9. Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations (by M. Bonforte, A. Figalli, J.L. Vazquez)
  10. A rigorous derivation from the kinetic Cucker-Smale model to the pressureless Euler system with nonlocal alignment (by A. Figalli, M-J. Kang)


  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. On the fine structure of the free boundary for the classical obstacle problem (by A. Figalli, J. Serra)
  11. On stable solutions for boundary reactions: a De Giorgi-type result in dimension 4+1 (by A. Figalli, J. Serra)
  12. Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains (by M. Bonforte, A. Figalli, J.L. Vazquez)