Skip to main content

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

  • 1865 Accesses


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

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

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Birkhäuser Verlag AG

About this chapter

Cite this chapter

(2009). Linear Elliptic Systems. In: Elliptic Equations: An Introductory Course. Birkhäuser Advanced Texts / Basler Lehrbücher. Birkhäuser Basel.

Download citation

Publish with us

Policies and ethics