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Session

NEE3: Nonlinear Evolution Equations and Applications Location: F420 Session Chair: Bogdan-Vasile Matioc Session Chair: Jürgen Saal Session Chair: Christoph Walker

Presentation 3

$\mathcal{H}^{\infty}$-calculus for the Laplacian on a 2D wedge domain Köhne Matthias, Saal Jürgen, Jascha Wolter Heinrich-Heine-Unversität, Germany We study the properties of the Laplace and Stokes operator on a 2D wedge domain $G$, subject to suitable boundary conditions. Through a transformation, the problem is transformed to a strip domain $\Omega$. On this transformed domain, we can apply the operator sum method for non-commuting operators to establish a bounded $\mathcal{H}^{\infty}$-calculus for the transformed operator operators in $L^p$. Using the Euclidean structures and their implied characterization of $\mathcal{H}^{\infty}-$calculus, we transfer this property back to the original wedge domain.