Laplace's equation

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In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties in 1786. This is often written as ∇ 2 f = 0 {\displaystyle \nabla ^{2}\!f=0} or Δ f = 0 , {\displaystyle \Delta f=0,} where Δ = ∇ ⋅ ∇ = ∇ 2 {\displaystyle \Delta =\nabla \cdot \nabla =\nabla ^{2}} is the Laplace operator, ∇ ⋅ {\displaystyle \nabla \cdot } is the divergence operator (also symbolized "div"), ∇ {\displaystyle \nabla } is the gradient operator (also symbolized "grad"), and...

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