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Journals and Conferences
We develop a method to prove that some critical levels for functionals invariant by symmetry obtained by minimax methods without any symmetry constraint are attained by symmetric critical points. It… (More)
We obtain boundary estimates for the gradient of solutions to elliptic systems with Dirichlet or Neumann boundary conditions and L1–data, under some condition on the divergence of the data. Similar… (More)
Article history: Received 4 September 2015 Accepted after revision 8 October 2015 Available online 6 November 2015 Presented by Haïm Brézis As a consequence of inequalities due to Bourgain–Brézis, we… (More)
We show that divergence-free L1 vector fields on a nilpotent homogeneous group of homogeneous dimension Q are in the dual space of functions whose gradient is in LQ. This was previously obtained on… (More)
The function spaces Dk(R) are introduced and studied. The definition of these spaces is based on a regularity property for the critical Sobolev spaces Ws,p(Rn), where sp = n, obtained by J. Bourgain,… (More)
This paper offers a variant of a proof of a borderline Bourgain-Brezis Sobolev embedding theorem on Rn. The authors use this idea to extend the result to real hyperbolic spaces Hn.
We study the existence of positive solutions for a class of nonlinear Schrödinger equations of the type −ε ∆u + V u = u in R , where N ≥ 3, p > 1 is subcritical and V is a nonnegative continuous… (More)
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.
We obtain estimates in Besov, Triebel–Lizorkin and Lorentz spaces of differential forms on Rn in terms of their L1 norm.
We study symmetry properties of least energy positive or nodal solutions of semilinear elliptic problems with Dirichlet or Neumann boundary conditions. The proof is based on symmetrizations in the… (More)