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Existence and regularity of minimizers of nonconvex integrals with growth

Pietro CeladaGiovanni CupiniMarcello Guidorzi — 2007

ESAIM: Control, Optimisation and Calculus of Variations

We show that local minimizers of functionals of the form Ω f ( D u ( x ) ) + g ( x , u ( x ) ) d x u u 0 + W 0 1 , p ( Ω ) , are locally Lipschitz continuous provided is a convex function with p - q growth satisfying a condition of qualified convexity at infinity and is Lipschitz continuous in . As a consequence of this, we obtain an existence result for a related nonconvex functional.

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