We show that local minimizers of functionals of the form ∫Ω[f(Du(x)) + g(x, u(x))] dx, u ∈0 + W 01,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.
Existence and regularity of minimizers of nonconvex integrals with p-q growth / CELADA P; G. CUPINI; GUIDORZI M. - In: ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS. - ISSN 1262-3377. - STAMPA. - 13:(2007), pp. 343-358. [10.1051/cocv:2007014]
Existence and regularity of minimizers of nonconvex integrals with p-q growth
CUPINI, GIOVANNI;
2007
Abstract
We show that local minimizers of functionals of the form ∫Ω[f(Du(x)) + g(x, u(x))] dx, u ∈0 + W 01,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.
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