Giovanni Cupini

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 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

Existence of Minimizers for Polyconvex and Nonpolyconvex Problems

q

The Role of Fundamental Solution in Potential and Regularity Theory for Subelliptic PDE

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

Global Lp estimates for degenerate Ornstein–Uhlenbeck operators

q

Local boundedness of solutions to quasilinear elliptic systems

q is larger than this threshold, counterexamples to the local boundedness and regularity of minimizers are known. In this paper, we prove the local boundedness of minimizers (and also of quasi-minimizers) under this stated limit condition. Some other general and limit growth conditions are also considered.