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

Abstract:

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

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