Divergence RHSOf Field add
DeGiorgi.divergenceRHSOfField_add
Plain-language statement
The divergence-form RHS is additive in the test slot.
Exact Lean statement
theorem divergenceRHSOfField_add
{Ω : Set E} {F : E → E} (hF : MemLp F 2 (volume.restrict Ω))
{v₁ v₂ : E → ℝ}
(hv₁ : MemW1pWitness 2 v₁ Ω)
(hv₂ : MemW1pWitness 2 v₂ Ω) :
divergenceRHSOfField F (hv₁.add hv₂) =
divergenceRHSOfField F hv₁ + divergenceRHSOfField F hv₂Formal artifact
Lean source
theorem divergenceRHSOfField_add {Ω : Set E} {F : E → E} (hF : MemLp F 2 (volume.restrict Ω)) {v₁ v₂ : E → ℝ} (hv₁ : MemW1pWitness 2 v₁ Ω) (hv₂ : MemW1pWitness 2 v₂ Ω) : divergenceRHSOfField F (hv₁.add hv₂) = divergenceRHSOfField F hv₁ + divergenceRHSOfField F hv₂ := by rw [divergenceRHSOfField, divergenceRHSOfField, divergenceRHSOfField, divergenceRHSIntegrandOfField_add] rw [integral_add (integrable_divergenceRHSIntegrandOfField hF hv₁) (integrable_divergenceRHSIntegrandOfField hF hv₂)] ring- Project
- DeGiorgi
- License
- Apache-2.0
- Commit
- 4c1b3077d378
- Source
- DeGiorgi/WeakFormulation/BilinearForm.lean:449-461
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Ae eq of tendsto e Lp Norm sub
BareFunction.ae_eq_of_tendsto_eLpNorm_sub
Plain-language statement
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Source project: DeGiorgi
Person-level attribution pending.
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Plain-language statement
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Person-level attribution pending.
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Plain-language statement
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Source project: DeGiorgi
Person-level attribution pending.