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. Itâ€¦ (More)

We obtain boundary estimates for the gradient of solutions to elliptic systems with Dirichlet or Neumann boundary conditions and L1â€“data, under some condition on the divergence of the data. Similarâ€¦ (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 onâ€¦ (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,â€¦ (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 SchrÃ¶dinger equations of the type âˆ’Îµ âˆ†u + V u = u in R , where N â‰¥ 3, p > 1 is subcritical and V is a nonnegative continuousâ€¦ (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 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 theâ€¦ (More)