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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 Pn i=1 1 pi . As a consequence, by mean of regularity results due to Lieberman [21], we obtain the local… (More)

- M. Amar, Virginia De Cicco, +5 authors Elvira Mascolo
- 2008

We prove a lower semicontinuity theorem for a polyconvex functional of integral form, related to maps u W R ! R in W 1;n.IRm/ with n m 2, with respect to the weak W 1;p-convergence for p > m 1, without assuming any coercivity condition.

- 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… (More)

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

We study the existence of Lipschitz minimizers of integral functionals

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