ActualPoissonEulerGradient.lean`

1 declarations, 0 contain sorry, 0 declared as axioms

The Euler-gradient error of the actual two-center Poisson difference

theorem OAI.RegularPointCoordinates.actual_poisson_euler_gradient line 21

Source documentation

The gradient of Gamma(f,v)-v is controlled by the two actual source budgets, including the curvature remainder and all singular mass.

theorem actual_poisson_euler_gradient {K : ℝ} {n : ℕ}
    (hX : NoncollapsedRCD K n X) [IsFiniteMeasureOnCompacts (hausdorff n X)]
    (hhessian : LocalPoissonHessianActionInput hX)
    (hproduct : LocalPoissonGradientProductInput hX)
    {κ B J C A Cχ epsilon r0 : ℝ} (hκ : 0 ≤ κ) (hK : -κ ≤ K)
    (hB : 0 ≤ B) (hJ : 0 ≤ J) (hCχ : 0 ≤ Cχ)
    (hA : 0 ≤ A) (hepsilon : 0 ≤ epsilon) (p₁ p₂ z : X)
    (S₁ : DyadicDistanceSources (hausdorff n X) hX.quadratic n κ p₁ r0)
    (S₂ : DyadicDistanceSources (hausdorff n X) hX.quadratic n κ p₂ r0)
    (T₁ : DyadicDistanceReplacements (hausdorff n X) hX.quadratic S₁ B J C)
    (T₂ : DyadicDistanceReplacements (hausdorff n X) hX.quadratic S₂ B J C)
    (i : ℕ)
…

Mentions: OAI.RegularPointCoordinates.NoncollapsedRCD, OAI.RegularPointCoordinates.hausdorff, OAI.RegularPointCoordinates.LocalPoissonHessianActionInput, OAI.RegularPointCoordinates.LocalPoissonGradientProductInput, OAI.RegularPointCoordinates.DyadicDistanceSources, OAI.RegularPointCoordinates.DyadicDistanceReplacements