Theorems · Theorem · potential theory

ContDiffAt.laplacian_add

∀ {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] {f₁ f₂ : E → F} {x : E},
  ContDiffAt ℝ 2 f₁ x →
    ContDiffAt ℝ 2 f₂ x → Laplacian.laplacian (f₁ + f₂) x = Laplacian.laplacian f₁ x + Laplacian.laplacian f₂ x

The Laplacian commutes with addition.

Defined in

Mathlib.Analysis.InnerProductSpace.Laplacian

Cited by

1 results in Mathlib

Foundations

Depth 245 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceFiniteDimensionalNormedAddCommGroupNormedSpace