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Session

PDE3: Partial Differential Equations Location: G227 Session Chair: Simon Markfelder Session Chair: Marlies Pirner

Presentation 1

Regularity for systems with symmetric gradients Linus Behn Bielefeld University, Germany The symmetric $p$-Laplace operator enters various models in mathematical physics, such as incompressible materials with power-type hardening and non-Newtonian fluids. In this and related models, the usual gradient $\nabla u$ of the displacement field $u$ is replaced by the symmetric gradient $\mathcal{E}u=\frac 12 (\nabla u +(\nabla u)^T)$, which results in a higher coupling of the system. We present regularity results for the solutions of such systems, including global and maximal regularity. This talk is based on joint work with Andrea Cianchi, Lars Diening, and Fa Peng.