Theorems · Theorem · potential theory

InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_complexPlane

∀ {F : Type u_3} [inst : NormedAddCommGroup F] [inst_1 : NormedSpace ℝ F] {e : ℂ} {s : Set ℂ} (f : ℂ → F),
  UniqueDiffOn ℝ s →
    e ∈ s →
      InnerProductSpace.laplacianWithin f s e =
        (iteratedFDerivWithin ℝ 2 f s e) ![1, 1] + (iteratedFDerivWithin ℝ 2 f s e) ![Complex.I, Complex.I]

Special case of the standard formula for functions on ℂ, with the standard real inner product structure.

Defined in

Mathlib.Analysis.InnerProductSpace.Laplacian

Cited by

0 results in Mathlib

Foundations

Depth 244 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace