Poincare Inequality implies Equivalent Norms
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I am currently working through the subject of Sobolev Spaces using the book 'Partial Differential Equations' by Lawrence Evans. After the result proving the Poincare Inequality it says the following in the book(page 266.) "In view of the Poincare Inequality, on $W_{0}^{1,p}(U)$ the norm $||DU||_{L^{p}}$ is equivalent to $||u||_{W^{1,p}(U)}$, if $U$ is bounded." Do you know the argument behind this statement?
functional-analysis inequality pde sobolev-spaces norm
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asked Oct 22 '13 at 10:12
Lucio D Lucio D
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