This article is dedicated to Emmanuele Di Benedetto, great mathematician, colleague,
friend. In the spirit to treat a subject that in the last years attracted the interest of several …

Gradient boundedness up to the boundary for solutions to Dirichlet and Neumann problems
for elliptic systems with Uhlenbeck type structure is established. Nonlinearities of possibly …

In the general vector-valued case N ≥ 1 N≥ 1, we prove the Lipschitz continuity of local
minimizers to some integrals of the calculus of variations of the form ∫ _ Ω g (x,| Du|)\, dx∫ …

We investigate the boundary regularity of minimizers of convex integral functionals with
nonstandard p, q-growth and with Uhlenbeck structure. We consider arbitrary convex …

We establish the higher differentiability and the higher integrability for the gradient of
vectorial minimizers of integral functionals with (p, q)-growth conditions. We assume that the …

In this paper, we consider minimizers of integral functionals of the type F (u):=∫ Ω [1 p (| D u|-
1)+ p+ f· u] dx for p> 1 in the vectorial case of mappings u: R n⊃ Ω→ RN with N≥ 1 …

Abstract For Ω⊆ R n an open and bounded region we consider solutions u∈ W loc 1, p
(x)(Ω; RN), with N> 1, of the p (x)-Laplacian system∇⋅(a (x)| D u| p (x)− 2 D u)= 0, ae x∈ Ω …

We consider weak solutions u of non-linear systems of partial differential equations.
Assuming that the system exhibits a certain kind of elliptic behavior near infinity we prove …

An optimal first-order global regularity theory, in spaces of functions defined in terms of
oscillations, is established for solutions to Dirichlet problems for the p-Laplace equation and …

We consider multidimensional variational integrals for vector-valued functions u: Rn⊃→ RN.
Assuming that the integrand satisfies the standard smoothness, convexity and growth …