Harmonic function

In Mathematical, a harmonic Fonction is a derivable function twice continuously : $F:\; U\; \backslash \; rightarrow\; \backslash \; mathbb\; \{R\}$ (Where U is open of $\backslash \; mathbb\; \{R\}\; ^n$) which satisfies the equation of Laplace:

$\backslash \; frac\; \{\backslash \; partial^2f\}\; \{\backslash \; partial\; x\_1^2\}\; +$

\ frac {\ partial^2f} {\ partial x_2^2} + \ cdots + \ frac {\ partial^2f} {\ partial x_n^2} = 0 On all U .

One also writes:

$\backslash \; nabla^2\; F\; =\; 0$ or $\backslash \; Delta\; F\; =\; 0$

A particular example is consisted of the functions real part and imaginary part deduced from a holomorphic Fonction.

A traditional problem concerning the harmonic functions is the Problème of Dirichlet: a function being given on the border of a Ouvert, can one continues prolong it in a harmonic function in all the interior of this open?

Random links:

Mende (Lozere) | Penelope Delta | George Raft | USAM Nimes | Crispin de Passe the Old one | Vague_bleue_d'Orix

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