Finiteness #
Part of the Caffarelli–Kohn–Nirenberg partial regularity proof.
theorem
CKN.caccioppoli_velocity_integral_ne_top
{Ω : Set Foundation.Parabolic.Vec3}
{I : Set ℝ}
{q : ℝ}
{u : Foundation.Parabolic.ParabolicPoint → Foundation.Parabolic.Vec3}
{Du : Foundation.Parabolic.ParabolicPoint → Fin 3 → Foundation.Parabolic.Vec3}
{p : Foundation.Parabolic.ParabolicPoint → ℝ}
{f : Foundation.Parabolic.ParabolicPoint → Foundation.Parabolic.Vec3}
(hsol : IsSuitableWeakSolutionIntegrable Ω I q u Du p f)
{x₀ : Foundation.Parabolic.Vec3}
{t₀ ρ : ℝ}
(hρ : 0 < ρ)
(hsub : closure (Foundation.Parabolic.parabolicCylinder x₀ t₀ ρ) ⊆ spaceTimeSet Ω I)
: