Theorems · Theorem · potential theory

InnerProductSpace.laplacian_eq_iteratedFDeriv_stdOrthonormalBasis

∀ {E : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E] [inst_2 : FiniteDimensional ℝ E]
  {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace ℝ F] (f : E → F),
  Laplacian.laplacian f = fun x =>
    ∑ i, (iteratedFDeriv ℝ 2 f x) ![(stdOrthonormalBasis ℝ E) i, (stdOrthonormalBasis ℝ E) i]

Standard formula, computing the Laplacian from the standard orthonormal basis of a real inner product space.

Defined in

Mathlib.Analysis.InnerProductSpace.Laplacian

Cited by

8 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupInnerProductSpaceFiniteDimensionalNormedAddCommGroupNormedSpace