Scientists / Open questions
Alessio Figalli
Optimal transport; partial differential equations; calculus of variations
2018 Fields Medal
28 questions
Critical anisotropic p-Laplacian classification in convex cones and the sharp weighted anisotropic Sobolev inequality beyond smooth uniformly convex norms and concave homogeneous weights
Optimal decay exponent and fractional weak Harnack inequality for solutions of strongly nonlocal equations with decaying source (Dipierro-Figalli-Valdinoci, 2014)
Optimal regularity of the pressure field of Brenier's weak solutions to the incompressible Euler equations: the semi-concavity conjecture and global-in-time estimates
Well-posedness of martingale solutions and Fokker–Planck equations beyond Figalli's hypotheses: sub-Sobolev spatially dependent degenerate diffusion, time-measurable uniformly elliptic coefficients, and stability without uniform density bounds