We prove sharp regularity results for a general class of functionals of the type w ↦ ∫ F (x, w,
Dw)\, dx, w↦∫ F (x, w, D w) dx, featuring non-standard growth conditions and non-uniform …

We prove sharp regularity theorems for minimisers of a class of variational integrals whose
integrand switches between two different types of degenerate elliptic phases, according to …

This paper deals with the fractional Sobolev spaces Ws, p. We analyze the relations among
some of their possible definitions and their role in the trace theory. We prove continuous and …

Definition 1 implies that local minimisers are automatically in W 1, p loc (Ω). We immediately
say that since all the regularity properties of local minimisers treated in this paper are local in …

The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

The class of non-autonomous functionals under study is characterized by the fact that the
energy density changes its ellipticity and growth properties according to the point; some …

We consider a class of non-uniformly nonlinear elliptic equations whose model is given by−
div (| D u| p− 2 D u+ a (x)| D u| q− 2 D u)=− div (| F| p− 2 F+ a (x)| F| q− 2 F) where p< q and a …

Regularity of minima: An invitation to the dark side of the calculus of variations | SpringerLink
Skip to main content Advertisement SpringerLink Log in Menu Find a journal Publish with us …

We consider non-linear elliptic equations having a measure in the right-hand side, of the
type div a (x, Du)= µ, and prove differentiability and integrability results for solutions. New …

Gradient estimates via non-linear potentials Page 1 Gradient estimates via non-linear
potentials Frank Duzaar, Giuseppe Mingione American Journal of Mathematics, Volume 133 …