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)
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.
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
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.