Partial regularity of minimizers of higher order integrals with (p,q)-growth

Abstract

Abstract. We consider higher order functionals of the formwhere the integrand f :is strictly quasiconvex and satisfies a non-standard growth condition. More precisely we assume that f fulfills the (p, q)-growth conditionwith γ, L > 0 and 1 < p ≤ q < min p + Mathematics Subject Classification. 49N60, 49N99, 49J45.

Partial regularity of strong local minimizers of quasiconvex integrals with (p, q)-growth

“…for the regularity. We refer to the forthcoming paper [45] for similar results in the higher order case. For n = N an important class of examples is given by the polyconvex integrands…”

Regularity for higher order quasiconvex problems with linear growth from below

“…These results were preceeded by work of FUSCO & HUTCHINSON [22] on the anisotropic polyconvex case, and certain related quasiconvex situations (see also [16]). Finally SCHEMM [37] extended the results of [38] to the k-th order case. We refer to [25] for a discussion of further regularity results for BV minimizers of convex and quasiconvex integrals, and to [35] for a survey of regularity results in Calculus of Variations and the related PDEs in the Sobolev context.…”

Partial regularity for minima of higher-order quasiconvex integrands with natural Orlicz growth

“…In the higher order case, the regularity theory for strongly k-quasiconvex integrands has been studied for instance by Guidorzi [39], Kronz [45], and Schemm [59]. Note the results of [16,9] show that higher-order quasiconvexity reduces to ordinary quasiconvexity under quantitative Lipschitz bounds on F ′ , so while these results do not directly apply we expect the higher order case to be essentially the same as the k = 1 setting.…”