Prescribing the Jacobian in critical spaces
نویسندگان
چکیده
We consider the Sobolev space X = W s,p(Sm;Sk−1). We prove the existence of a robust distributional Jacobian Ju for u ∈ X provided sp ≥ k−1; this generalizes a result of Bourgain, Brezis and the second author [10], where the case m = k is considered. In the critical case where sp = k − 1, we identify the image of the map X 3 u 7→ Ju. This extends a result of Alberti, Baldo and Orlandi [2] for s = 1 and p = k−1. We also present a new, analytical, dipole construction method.
منابع مشابه
The Characterization of the Regularity of the Jacobian Determinant in the framework of Potential spaces
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