Existence and regularity of minimizers of nonconvex integrals with p-q growth
ESAIM: Control, Optimisation and Calculus of Variations, Volume 13 (2007) no. 2, pp. 343-358.

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

DOI: 10.1051/cocv:2007014
Classification: 49N60, 49J10
Keywords: nonstandard growth, existence, Lipschitz continuity
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Celada, Pietro; Cupini, Giovanni; Guidorzi, Marcello. Existence and regularity of minimizers of nonconvex integrals with $p-q$ growth. ESAIM: Control, Optimisation and Calculus of Variations, Volume 13 (2007) no. 2, pp. 343-358. doi : 10.1051/cocv:2007014. http://www.numdam.org/articles/10.1051/cocv:2007014/

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