Source-pinned research
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This index contains 41 research declarations. Search 10,000 more complete Mathlib declarations.
41 results
Clear filtersHeat.integral_mul_exp_neg_sq_Ici_zero
Plain-language statement
Evaluation of ∫₀^∞ z exp(-z²) dz = 1/2.
Source project: PDE
Person-level attribution pending.
Heat.integral_split_near_far
Project documentation
Helper lemma for splitting integrals into near and far regions.
Source project: PDE
Person-level attribution pending.
integral_smul_aezero_tsupport
Plain-language statement
If f vanishes a.e. on U and g is supported in U, then ∫ f • g ∂μU = 0.
Source project: PDE
Person-level attribution pending.
integral_tendsto_of_Lploc_tendsto
Plain-language statement
If f i converges to g in Lᵖ(U), then for any test function ψ ∈ C_c^∞(U), the integrals ∫ f i * ψ ∂μU converge to ∫ g * ψ ∂μU.
Source project: PDE
Person-level attribution pending.
IsOpen.ae_eq_of_integral_contDiff_smul_eq
Project documentation
If ∫ ψ · f = ∫ ψ · g for all ψ ∈ Cc^∞(U), then f =ᵃᵉ g on U. This is the du Bois-Reymond lemma, the key uniqueness engine for weak derivatives.
Source project: PDE
Person-level attribution pending.
NNReal.rpow_sum_le_sum
Plain-language statement
A discrete Minkowski inequality: for p ≥ 1 and a finite sequence a : Fin n → ℝ≥0, the ℓᵖ norm of a is bounded above by the sum of its entries.
Source project: PDE
Person-level attribution pending.