Scientists / Open questions
阿莱西奥·菲加利
Alessio Figalli
最优输运、偏微分方程、变分法
2018 年菲尔兹奖
28 个问题
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