Theorems · Theorem · potential theory

tensorIteratedFDerivWithinTwo_eq_iteratedFDerivWithin

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {e : E}
  {s : Set E} (f : E → F),
  UniqueDiffOn 𝕜 s →
    e ∈ s →
      ∀ (e₁ e₂ : E), (tensorIteratedFDerivWithinTwo 𝕜 f s e) (e₁ ⊗ₜ[𝕜] e₂) = (iteratedFDerivWithin 𝕜 2 f s e) ![e₁, e₂]

Expression of tensorIteratedFDerivTwo in terms of iteratedFDerivWithin.

Defined in

Mathlib.Analysis.InnerProductSpace.Laplacian

Cited by

1 results in Mathlib

Foundations

Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace