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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)

- Giovanni Cupini, Paolo Marcellini, Elvira Mascolo
- J. Optimization Theory and Applications
- 2015

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)

- Giovanni Cupini, Elvira Mascolo
- SIAM J. Control and Optimization
- 2005

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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