Elvira Mascolo

Regularity of minimizers of vectorial integrals with p - q growth

Local Lipschitz continuity of local minimizers of vectorial integrals ∫Ωf(x,Du(x))dx is proved when f satisfies p−q growth condition and ξ↦f(x,ξ) is convex. The uniform convexity and the radial structure condition with respect to the last variable are assumed only at infinity.

Local boundedness of minimizers of integrals of the calculus of variations

In this paper we prove the local boundedness of minimizers of integral functionals with non-standard growth conditions.

Harnack inequality for minimizers of integral functionals with general growth conditions

We prove the Harnack inequality for positive minimizers of a class of integral functionals with non-standard growth conditions.

Local Boundedness for Vector Valued Minimizers of Anisotropic Functionals

For variational integrals F(u) = ∫ Ω f(x,Du) dx defined on vector valued mappings u : Ω ⊂ Rn → RN , we establish some structure conditions on f that enable us to prove local boundedness for minimizers u ∈ W 1,1(Ω;RN ) of F . These structure conditions are satisfied in three remarkable examples: f(x,Du) = g(x, |Du|), f(x,Du) = n ∑ j=1 gj(x, |uxj |) and f(x,Du) = a(x, |(ux1 , . . . , uxn−1)|) + b(x, |uxn |), for suitable convex functions t→ g(x, t), t→ gj(x, t), t→ a(x, t) and t→ b(x, t).

Local Boundedness of Minimizers with Limit Growth Conditions

The energy integral of the calculus of variations, which we consider in this paper, has a limit behavior when the maximum exponent

Weak lower semicontinuity for non coercive polyconvex integrals

q

Existence of Minimizers for Polyconvex and Nonpolyconvex Problems

q, in the growth estimate of the integrand, reaches a threshold. In fact, if