Lipschitz regularity of the minimizers of autonomous integral functionals with discontinuous non-convex integrands of slow growth

Mariconda, Carlo; Treu, Giulia
May 2007
Calculus of Variations & Partial Differential Equations;May2007, Vol. 29 Issue 1, p99
Academic Journal
Let $$L(x,\xi):\mathbb{R}^N\times\mathbb{R}^N\to \mathbb{R}$$ be a Borelian function and let ( P) be the problem of minimizing among the absolutely continuous functions with prescribed values at a and b. We give some sufficient conditions that weaken the classical superlinear growth assumption to ensure that the minima of ( P) are Lipschitz. We do not assume convexity of L w.r. to $$\xi$$ or continuity of L.


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