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Part of the book series: Birkhäuser Advanced Texts / Basler Lehrbücher ((BAT))

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Abstract

Sometimes, in many physical situations, one has not only to look for a scalar u but for a vector u = (u1,... ,um). (In what follows a bold letter will always denote a vector.) This could be a position in space, a displacement, a velocity... So one is in need to introduce systems of equations. The simplest one is of course the one consisting in m copies of the Dirichlet problem, that is to say

$$ \left\{ \begin{gathered} - \Delta u^1 = f^1 in \Omega , \hfill \\ \cdots \cdots \cdots \cdots \hfill \\ - \Delta u^m = f^m in \Omega , \hfill \\ u = \left( {u^1 , \ldots u^m } \right) = 0 on \partial \Omega . \hfill \\ \end{gathered} \right. $$
((13.1))

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© 2009 Birkhäuser Verlag AG

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(2009). Linear Elliptic Systems. In: Elliptic Equations: An Introductory Course. Birkhäuser Advanced Texts / Basler Lehrbücher. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9982-5_13

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