Embeddings for the space on sets of finite perimeter
2019 ◽
Vol 150
(5)
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pp. 2442-2461
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Keyword(s):
Open Set
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AbstractGiven 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.
2007 ◽
Vol 53
(3-4)
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pp. 413-435
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2003 ◽
Vol 3
(3)
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pp. 419-441
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2003 ◽
Vol 3
(3)
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pp. 443-461
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2011 ◽
Vol 38
(1)
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pp. 71-84
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Keyword(s):