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- Sagun Chanillo, Jean Van Schaftingen
- 2008

We show that divergence-free L 1 vector fields on a nilpotent homogeneous group of homogeneous dimension Q are in the dual space of functions whose gradient is in L Q. This was previously obtained on R n by Bourgain and Brezis.

The function spaces D k (R n) are introduced and studied. The definition of these spaces is based on a regularity property for the critical Sobolev spaces W s,p (R n), where sp = n, obtained The spaces D k (R n) contain all the critical Sobolev spaces. They are embedded in BMO(R n), but not in VMO(R n). Moreover, they have some extension and trace… (More)

- Augusto C Ponce, Jean Van Schaftingen
- 2009

For every 2 < p < 3, we show that u ∈ W 1,p (B 3 ; S 2) can be strongly approximated by maps in C ∞ (B 3 ; S 2) if, and only if, the distribu-tional Jacobian of u vanishes identically. This result was originally proved by Bethuel-Coron-Demengel-Hélein, but we present a different strategy which is motivated by the W 2,p-case.

We obtain estimates in Besov, Lizorkin-Triebel and Lorentz spaces of differential forms on R n in terms of their L 1 norm.

We give an explicit sequence of polarizations such that for every measurable function, the sequence of iterated polarizations converge to the symmetric rearrangement of the initial function.

- Sagun Chanillo, Jean Van Schaftingen
- 2016

Dedicated to Vladimir Maz'ya on the occasion of his 70th birthday, with high esteem and friendship Abstract. We study various questions related to the best constants in the

- Jean Van Schaftingen
- The American Mathematical Monthly
- 2013

We obtain boundary estimates for the gradient of solutions to elliptic systems with Dirichlet or Neumann boundary conditions and L 1 –data, under some condition on the divergence of the data. Similar boundary estimates are obtained for div–curl and Hodge systems.

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