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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.
4
votes
Optimal condition for the weak convergence of the jacobian determinant
If $q=n,$ then $\operatorname*{det}\nabla u \in L^1,$ but we have only convergence in distributions, i.e
$$\operatorname*{det} \nabla u_{k} \rightharpoonup \operatorname*{det} \nabla u \quad \text{ i …