| import Mathlib | |
| import OAI.Analysis.HardSphere.FormDomain.EnergyInsertionJet | |
| import OAI.Analysis.HardSphere.Geometry.CoordinateLineConsSucc | |
| namespace OAI | |
| noncomputable section | |
| open MeasureTheory Filter Set | |
| open scoped ENNReal Topology BigOperators | |
| open scoped BigOperators ComplexConjugate | |
| open MeasureTheory ProbabilityTheory Filter Set | |
| open scoped ENNReal NNReal Topology BigOperators | |
| open MeasureTheory ProbabilityTheory Real Complex | |
| open scoped ENNReal ComplexConjugate | |
| open ProbabilityTheory | |
| namespace HardSphere | |
| open MeasureTheory Set Filter | |
| open scoped ComplexConjugate | |
| lemma SmoothMultiplier.normalized_insertion {n : ℕ} {L : Length} {a C : ℝ} | |
| (f : SmoothMultiplier (n+1) L) (hc : InsertionClearance a f) | |
| (hr : ∀ X, conj (f.toFun X)=f.toFun X) | |
| (hn : ∀ Y : Configuration n L, ∫ x : Torus L, ‖f.toFun (Fin.cons x Y)‖^2=1) | |
| (hC : ∀ Y : Configuration n L, | |
| ∑ p : Direction (n+1), ∫ x : Torus L, ‖coordDerivative (n+1) L f.toFun p (Fin.cons x Y)‖^2≤C) | |
| {u : Jet n L} (hu : u∈dirichletDomain n L a) : | |
| f.insertionJet u∈dirichletDomain (n+1) L a ∧ | |
| ‖(f.insertionJet u).1‖=‖u.1‖ ∧ energy (f.insertionJet u)≤energy u+C*‖u.1‖^2 := by | |
| refine ⟨f.insertionJet_mem_domain hc hu,?_,?_⟩ | |
| · exact f.norm_insertionScalar hn u.1 | |
| · exact f.energy_insertionJet_le hn (f.insertion_orthogonal hr hn) C hC u | |
| end HardSphere | |
| end | |
| end OAI | |