Regularity of minima: An invitation to the dark side of the calculus of variations | SpringerLink
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In this paper we consider integral functionals of the form with convex integrand satisfying (p,
q) growth conditions. We prove local higher differentiability results for bounded minimizers of …

In this paper we consider integral functionals of the form with convex integrand satisfying p
growth conditions with respect to the gradient variable. As a novel feature, the dependence …

We give a regularity result for local minimizers u: Ω ⊂ R^ 3 → R^ 3 u: Ω⊂ R 3→ R 3 of a
special class of polyconvex functionals. Under some structure assumptions on the energy …

We prove the higher differentiability and the higher integrability of the a priori bounded local
minimizers of integral functionals of the form ℱ⁢(v, Ω)=∫ Ω f⁢(x, D⁢ v⁢(x))⁢ dx, with convex …

We consider polyconvex functionals of the Calculus of Variations defined on maps from the
three-dimensional Euclidean space into itself. Counterexamples show that minimizers need …

We prove a new energy or Caccioppoli type estimate for minimisers of the model
functional∫ Ω| Du| 2+(det Du) 2, where Ω⊂ 2 and u: Ω→ 2. We apply this to establish C∞ …

Let us consider vector valued mappings u: Ω⊂ Rn→ Rn; when x∈ Ω, it turns out that Du (x)
is an× n matrix. For i∈{1,..., n} we set Mi (Du) to be the vector containing all the minors i× i …

We construct a trace preserving operator which improves the integrability of functions in
Sobolev classes refining the ones available in literature. As applications, we prove a C 1, α …

We deal with maps u: Ω⊂ Rn→ RN minimizing variational integrals∫ Ω f (x, Du (x)) dx.
Under suitable assumptions on f, we prove upper and lower bounds for every component uβ …