File size: 833 Bytes
67aee1d | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 | import Mathlib
import OAI.Analysis.HardSphere.Geometry.ScalarNormSqIntegral
import OAI.Analysis.HardSphere.Cutoffs.DifferentialFormula
namespace OAI
section
section
noncomputable section
open MeasureTheory Filter Set
open scoped Topology ENNReal BigOperators
open scoped RealInnerProductSpace
namespace HardSphere
lemma IsGroundVector.ae_gradient_phase {N : ℕ} {L : Length} {a : ℝ} {u : Jet N L}
(hu : IsGroundVector N L a u) (p : Direction N) :
∀ᵐ X ∂volume, u.2 p X = u.1 X / (‖u.1 X‖ : ℂ) * (modulusJet u).2 p X := by
filter_upwards [hu.ae_norm_modulusPartial p, coe_modulusPartial u.1 (u.2 p)] with X h1 h2
change u.2 p X = u.1 X / (‖u.1 X‖ : ℂ) * modulusPartial u.1 (u.2 p) X
rw [h2]
exact ComplexRegularization.phase_differential_of_norm_eq _ _ h1
end HardSphere
end
end
end
end OAI
|