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We prove boundedness of minimizers of energy-functionals, for instance of the anisotropic type (1.1) below, under sharp assumptions on the exponents pi in terms of p * : the Sobolev conjugate exponent of p; i.e., p * = np n−p , 1 p = 1 n P n i=1 1 p i. As a consequence, by mean of regularity results due to Lieberman [21], we obtain the local… (More)

The energy-integral of the calculus of variations (1.1), (1.2) below has a limit behavior when q = np/(n − p), where p is the harmonic average of the exponents pi, i = 1,. .. , n. In fact, if q is larger than in the stated equality, counterexamples to the local boundedness and regularity of minimizers are known. In this paper we prove the local boundedness… (More)

We study the existence of Lipschitz minimizers of integral functionals I(u) = Ω ϕ(x, det Du(x)) dx where Ω is an open subset of R N with Lipschitz boundary, ϕ : Ω×(0, +∞) → [0, +∞) is a continuous function and u ∈ W 1,N (Ω, R N), u(x) = x on ∂Ω. We consider both the cases of ϕ convex and nonconvex with respect to the last variable. The attainment results… (More)

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