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A Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function itself and its derivatives up to a given order.
2
votes
Dependence of the constant in Korn's inequality on the domain
I have not worked out the details, but this may be a way to find an answer:
The kernel of your operator $\mathcal E$ consists of rigid body motions, namely translations, reflexions and rotations. Thi …