This paper is essentially a survey on grand and small Lebesgue spaces, which are
rearrangement-invariant Banach function spaces of interest not only from the point of view of …

Blow-up analysis of a Finsler–Liouville equation in two dimensions Page 1 J. Differential
Equations 252 (2012) 1668–1700 Contents lists available at ScienceDirect Journal of …

We study the global in time existence of solutions to the parabolic-elliptic Patlak-Keller-
Segel system of multi-species populations. We prove that if the initial mass satisfies an …

We consider the problem of finding the optimal constant for the embedding of the space W^
2, 1 _ Δ, 0 (Ω):={u ∈ W^ 1, 1 _0 (Ω)\,\big|\, there exists {u_k\} ⊂ C_c^ ∞ (Ω) st ‖ Δ u_k-Δ u …

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 …

In this article we present recent results on optimal embeddings, and associated PDEs, of the
space of functions whose distributional Laplacian belongs to L1. We discuss sharp …

We consider quasilinear elliptic 2 m-order (m⩾ 2) partial differential equations whose
prototype is∑| α|= m (− 1)| α| D α (| D mu| p− 2 D α u)−∑| α|= 1 D α (| D u| q− 2 D α u)= f (x) …

In this article we extend the author's previous results on the existence of bounded
generalized solutions of a Dirichlet problem for nonlinear elliptic fourth-order equations with …

We prove some existence and regularity results for solutions of equations in the form -
div(a(x,u)∇u)=f, where a(x,s):Ω*\mathbbR→\mathbbR is a bounded Carath\'eodory function …

For Ω⊂ R2 a bounded open set with C1 boundary, we study the regularity of the variational
solution v∈ W1, 2 0 (Ω) to the quasilinear elliptic equation of Leray-Lions− div A (x,∇ v)= f …