We show sharp local a priori estimates and regularity results for possibly degenerate non-
linear elliptic problems, with data not lying in the natural dual space. We provide a precise …

In this paper we prove the L∞-boundedness of solutions of the quasilinear elliptic equation
Au\,= f (x, u, ∇ u) &\quad in\, Ω,\∂ u ∂ ν\,= g (x, u) &\quad on\, ∂ Ω, where A is a second …

A sharp rearrangement estimate for the nonlinear Havin-Maz'ya potentials is established. In
particular, this estimate leads to a characterization of those rearrangement invariant spaces …

A sharp integrability condition on the right-hand side of the p-Laplace system for all its
solutions to be continuous is exhibited. Their uniform continuity is also analyzed and …

Calderón-Zygmund theory is a classical topic in the analysis of partial differential equations,
and deals with determining, possibly in a sharp way, the integrability and differentiability …

We prove sharp embedding inequalities for certain reduced Sobolev spaces that arise
naturally in the context of Dirichlet problems with L 1 data. We also find the optimal target …

Solutions to the n-Laplace equation with a right-hand side f are considered. We exhibit the
largest rearrangement-invariant space to which f has to belong for every local weak solution …

The problem is addressed of the maximal integrability of the gradient of solutions to
quasilinear elliptic equations, with merely measurable coefficients, in two variables. Optimal …

We develop a new method that enables us to solve the open problem of characterizing
discrete inequalities for kernel operators involving suprema. More precisely, we establish …

In this article, we establish a comparison result through symmetrization for solutions to some
problems with general growth in the gradient. This allows to get sharp estimates for the …