Scientists / Open questions

查尔斯·费弗曼

Charles Louis Fefferman

调和分析、偏微分方程

1978 年菲尔兹奖

13 个问题

Sharp critical coupling and sharp stability constants for the pseudo-relativistic many-body Coulomb Hamiltonian
Linear extension operators for Sobolev spaces on weighted trees: the endpoint cases $p=1$ and $p=\infty$ , the inhomogeneous space $W^{1,p}(T)$ , non-radially-symmetric weights, and the planar $\dot W^{2,p}(\mathbb{R}^2)$ extension problem for $1<p<2$
Rigorous justification of vortex-line dynamics in the 3D Euler equations: construction of almost-sharp vortex tubes and derivation of the vortex filament equation
The sharp $H$ -stability constant of many-body Pauli--Fierz matter: the $\varepsilon(Z)\le\mathrm{const}\cdot Z$ conjecture
The omitted details in Fefferman's linear interpolation and extrapolation operators: an explicit bounded-depth construction for finite sets and the $m=1$ case of the Banach-limit passage
The oscillatory fourth term in the ground-state energy of large atoms: open quantitative problems on the Weyl sums of Córdoba–Fefferman–Seco (1995)
Semialgebraic sections of semialgebraic $C^m$ -jet bundles in dimensions $n \ge 3$ at fixed smoothness $m \ge 2$
Logarithmic and nonlocal terms in the boundary asymptotic expansion of the harmonic projection kernels of the Bergman metric on strictly pseudoconvex domains
The spin of the ground state of a large atom: sharp bounds and extensions to molecules
Bounded linear Sobolev $L^{2,p}$ extension for arbitrary finite subsets of the plane when $1<p<2$
The Sharp Interpolation Algorithm for $C^m(\mathbb{R}^n)$ (Fefferman's Conjecture 2): computing $(1+\epsilon)$ -optimal interpolants of finite data with near-linear work
Finite-time pinch-off of capillary jets in the Navier–Stokes equations with surface tension
Uniform-in-surface-tension local well-posedness and desingularization control for 2D water waves with surface tension beyond the Rayleigh–Taylor-positive regime

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Sharp critical coupling and sharp stability constants for the pseudo-relativistic many-body Coulomb Hamiltonian

Linear extension operators for Sobolev spaces on weighted trees: the endpoint cases p=1p=1p=1 and p=∞p=\inftyp=∞, the inhomogeneous space W1,p(T)W^{1,p}(T)W1,p(T), non-radially-symmetric weights, and the planar W˙2,p(R2)\dot W^{2,p}(\mathbb{R}^2)W˙2,p(R2) extension problem for 1<p<21<p<21<p<2

Rigorous justification of vortex-line dynamics in the 3D Euler equations: construction of almost-sharp vortex tubes and derivation of the vortex filament equation

The sharp HHH-stability constant of many-body Pauli--Fierz matter: the ε(Z)≤const⋅Z\varepsilon(Z)\le\mathrm{const}\cdot Zε(Z)≤const⋅Z conjecture

The omitted details in Fefferman's linear interpolation and extrapolation operators: an explicit bounded-depth construction for finite sets and the m=1m=1m=1 case of the Banach-limit passage

The oscillatory fourth term in the ground-state energy of large atoms: open quantitative problems on the Weyl sums of Córdoba–Fefferman–Seco (1995)

Semialgebraic sections of semialgebraic CmC^mCm-jet bundles in dimensions n≥3n \ge 3n≥3 at fixed smoothness m≥2m \ge 2m≥2

Logarithmic and nonlocal terms in the boundary asymptotic expansion of the harmonic projection kernels of the Bergman metric on strictly pseudoconvex domains

The spin of the ground state of a large atom: sharp bounds and extensions to molecules

Bounded linear Sobolev L2,pL^{2,p}L2,p extension for arbitrary finite subsets of the plane when 1<p<21<p<21<p<2

The Sharp Interpolation Algorithm for Cm(Rn)C^m(\mathbb{R}^n)Cm(Rn) (Fefferman's Conjecture 2): computing (1+ϵ)(1+\epsilon)(1+ϵ)-optimal interpolants of finite data with near-linear work

Finite-time pinch-off of capillary jets in the Navier–Stokes equations with surface tension

Uniform-in-surface-tension local well-posedness and desingularization control for 2D water waves with surface tension beyond the Rayleigh–Taylor-positive regime

Linear extension operators for Sobolev spaces on weighted trees: the endpoint cases $p=1$ and $p=\infty$ , the inhomogeneous space $W^{1,p}(T)$ , non-radially-symmetric weights, and the planar $\dot W^{2,p}(\mathbb{R}^2)$ extension problem for $1<p<2$

The sharp $H$ -stability constant of many-body Pauli--Fierz matter: the $\varepsilon(Z)\le\mathrm{const}\cdot Z$ conjecture

The omitted details in Fefferman's linear interpolation and extrapolation operators: an explicit bounded-depth construction for finite sets and the $m=1$ case of the Banach-limit passage

Semialgebraic sections of semialgebraic $C^m$ -jet bundles in dimensions $n \ge 3$ at fixed smoothness $m \ge 2$

Bounded linear Sobolev $L^{2,p}$ extension for arbitrary finite subsets of the plane when $1<p<2$

The Sharp Interpolation Algorithm for $C^m(\mathbb{R}^n)$ (Fefferman's Conjecture 2): computing $(1+\epsilon)$ -optimal interpolants of finite data with near-linear work