Calculus of Variations and Geometric Measure Theory

P. Celada - G. Cupini - M. Guidorzi

Existence and regularity of minimizers of nonconvex integrals with $p-q$ growth

created by cupini on 11 Jul 2005
modified on 15 May 2007


Published Paper

Inserted: 11 jul 2005
Last Updated: 15 may 2007

Journal: ESAIM Control Optim. Calc. Var.
Volume: 13
Number: 2
Pages: 343-358
Year: 2007


We show that local minimizers of functionals of the form \begin{displaymath} \int\Omega \leftf(Du(x)) + g(x\,,u(x))\right\,dx, \qquad u \in u0 + W0{1,p}(\Omega), \end{displaymath} 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.

Keywords: existence, lipschitz continuity, Nonstandard growth