# American Institute of Mathematical Sciences

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October  2013, 6(5): 1259-1275. doi: 10.3934/dcdss.2013.6.1259

## $H^{\infty}$-calculus for a system of Laplace operators with mixed order boundary conditions

 1 TU Darmstadt, FB Mathematik, Schlossgartenstr 7, D-64289 Darmstadt, Germany, Germany, Germany

Received  January 2012 Revised  February 2012 Published  March 2013

In this paper we prove that the $L^p$ realisation of a system of Laplace operators subjected to mixed first and zero order boundary conditions admits a bounded $H^{\infty}$-calculus. Furthermore, we apply this result to the Magnetohydrodynamic equation with perfectly conducting wall condition.
Citation: Matthias Geissert, Horst Heck, Christof Trunk. $H^{\infty}$-calculus for a system of Laplace operators with mixed order boundary conditions. Discrete & Continuous Dynamical Systems - S, 2013, 6 (5) : 1259-1275. doi: 10.3934/dcdss.2013.6.1259
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