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

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  • 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.
    Mathematics Subject Classification: Primary: 35K51; Secondary: 76W05.

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