A Harmonic replacement exists

theorem aHarmonic_replacement_exists    {Ω : Set E} (hd : 2 ≤ d)    (hΩ : IsOpen Ω) (hΩ_bdd : Bornology.IsBounded Ω)    {u : E → ℝ}    (A : EllipticCoeff d Ω)    (hu : MemW1p 2 u Ω) :    ∃ h : E → ℝ,      IsHomogeneousWeakSolution A h ∧      MemW01p 2 (fun x => h x - u x) Ω := by  have hF0 : MemLp (fun _ : E => (0 : E)) 2 (volume.restrict Ω) := by    exact MeasureTheory.MemLp.zero' (p := (2 : ENNReal)) (μ := volume.restrict Ω)  obtain ⟨h, hh_mem, hdiff, hweak⟩ :=    dirichletProblem_exists_of_divergenceData hd hΩ hΩ_bdd A hu hF0  refine ⟨h, ?_, hdiff⟩  refine ⟨hh_mem, ?_⟩  intro hh φ hφ hφw  have hEq := hweak hh φ hφ hφw  simpa [divergenceRHSOfField, divergenceRHSIntegrandOfField] using hEq