We show that local minimizers of functionals of the form int_Omega [f(Du(x)) + g(x,u(x))]dx, u in u_0 + W_0^{1,p}(Omega), 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.
P. Celada, G. Cupini, M. Guidorzi (2007). Existence and regularity of minimizers of nonconvex integrals with p-q growth. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 13, 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 int_Omega [f(Du(x)) + g(x,u(x))]dx, u in u_0 + W_0^{1,p}(Omega), 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.File in questo prodotto:
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