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Embeddings for the space $LD_\gamma ^{p}$ on sets of finite perimeter

  • Nikolai V. Chemetov (a1) and Anna L. Mazzucato (a2)


Given an open set with finite perimeter $\Omega \subset {\open R}^n$ , we consider the space $LD_\gamma ^{p}(\Omega )$ , $1\les p<\infty $ , of functions with pth-integrable deformation tensor on Ω and with pth-integrable trace value on the essential boundary of Ω. We establish the continuous embedding $LD_\gamma ^{p}(\Omega )\subset L^{pN/(N-1)}(\Omega )$ . The space $LD_\gamma ^{p}(\Omega )$ and this embedding arise naturally in studying the motion of rigid bodies in a viscous, incompressible fluid.



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