The Jacobian determinant revisited

By Haim Brezis, Hoai-Minh Nguyen. 2011

72 citations recorded by the source corpus.

This paper is devoted to the study of the Jacobian determinant of a map g from Ω, a smooth bounded open subset of RN , into RN (N ≥ 2). More generally, Ω could be a smooth bounded open subset of an N -dimensional manifold. Starting with the seminal work of C. B. Morrey [27], Y. Reshetnyak [32], and J. Ball [1], it has been known that one can define the distributional Jacobian determinant Det(∇g) under fairly weak assumption on g; in particular, it is defined for all maps g ∈ W 1, N2 N+1 (Ω) and also for all

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d18234decd510fd49f8e6526e2761b6c8393aee5

How researchers see this paper

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In Applied Mathematics

1. E. Lenzmann
2. Armin Schikorra
3. Katarzyna Mazowiecka
4. Giampiero Palatucci

In Geometry and Topology

1. E. Lenzmann
2. Armin Schikorra

Citations in the corpus

• A Sobolev non embedding (2015, background): “In connection with his work on distributional Jacobians [3], H. Brezis asked us whether the inclusion W 1 / 2 , 3 ((0 , 1)) ⊂ W 1 / 2 , 2 ((0 , 1)) holds.”
• Sharp commutator estimates via harmonic extensions (2016, methodology): “H. Brezis and H. Nguyen, The Jacobian determinant revisited, Invent.”