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

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We show that local minimizers of functionals of the form ∫ Ω f(Du(x))+g(x,u(x))dx, u∈u 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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     author = {Celada, Pietro and Cupini, Giovanni and Guidorzi, Marcello},
     title = {Existence and regularity of minimizers of nonconvex integrals with $p-q$ growth},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {343--358},
     publisher = {EDP-Sciences},
     volume = {13},
     number = {2},
     year = {2007},
     doi = {10.1051/cocv:2007014},
     mrnumber = {2306640},
     zbl = {1124.49031},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2007014/}
}
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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, Tome 13 (2007) no. 2, pp. 343-358. doi: 10.1051/cocv:2007014

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