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Rectifiability structure of sets of finite perimeter and discontinuities of functions of bounded variation, existence of perimeter minimizing sets

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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12 - Sets of Finite Perimeter and Functions of Bounded Variation

Summary

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

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12 - Sets of Finite Perimeter and Functions of Bounded Variation

Summary

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