Slicewise L² bound of cutoff1 #
‖cutoff1(t)‖²_{L²(𝕋²)} ≤ P² ‖∇T(t)‖²_{L²(𝕋²)}, from the pointwise bound
sb_cutoff1_abs_le (a Bochner integral dominated by an integrable function needs no integrability
of the dominated function).
theorem
AVenhance.Infra.Section5.Contracts.sb_l2NormSq_cutoff1_le
{β : ℝ}
(I : Ingredients β)
{Φ : ℕ → ℝ → Homogenization.Vec 2 → ℝ}
(hΦ : IsStreamSeq I Φ)
{m : ℕ}
(hm : 2 ≤ m)
{κ : ℝ}
(hκ : 0 ≤ κ)
{T : ℝ → Homogenization.Vec 2 → ℝ}
{t : ℝ}
(hTt : ContDiff ℝ (↑⊤) (T t))
: