: Mathématiques: Laplace's equation

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Laplace's equation

In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties. This is often written as
${\\displaystyle \ abla ^{2}\\!f=0}$ or ${\\displaystyle \\Delta f=0,}$
where ${\\displaystyle \\Delta =\ abla \\cdot \ abla =\ abla ^{2}}$ is the Laplace operator, ${\\displaystyle \ abla \\cdot }$ is the divergence operator (also symbolized "div"), ${\\displaystyle \ abla }$ is the gradient operator (also symbolized "grad"), and ${\\displaystyle f(x,y,z)}$ is a twice-differentiable real-valued function. The Laplace operator therefore maps a scalar function to another scalar function.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Laplace%27s_equation)