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mathematical physics > special function > harmonic function

mathematical analysis > functional analysis > special function > harmonic function

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harmonic function

In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function ${\\displaystyle f:U\ o \\mathbb {R} ,}$ where $U$ is an open subset of ${\\displaystyle \\mathbb {R} ^{n},}$ that satisfies Laplace's equation, that is,

${\\displaystyle {\ rac {\\partial ^{2}f}{\\partial x_{1}^{2}}}+{\ rac {\\partial ^{2}f}{\\partial x_{2}^{2}}}+\\cdots +{\ rac {\\partial ^{2}f}{\\partial x_{n}^{2}}}=0}$

everywhere on $U$ . This is usually written as

${\\displaystyle \ abla ^{2}f=0}$

or

${\\displaystyle \\Delta f=0}$

special function

harmonic measure

fonction harmonique

francés

URI

http://data.loterre.fr/ark:/67375/PSR-H7WG59FS-L

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