The result of this paper yields a maximum principle for the components of surfaces whose distortion by a certain matrix are minimizers of a dominance functional of a parametric functional with dominant area term within boundary value classes , termed -surfaces. Finally we derive a compactness result for sequences of -surfaces in , which serves as a preparation for the forthcoming article [R. Jakob, Unstable extremal surfaces of the “Shiffman functional” spanning rectifiable boundary curves, Calc. Var., submitted for publication] whose aim is a proof of a sufficient condition for the existence of extremal surfaces of which do not furnish global minima of within the class of -surfaces spanning an arbitrary closed rectifiable boundary curve that merely has to satisfy a chord-arc condition.
Cite this article
Ruben Jakob, A “quasi maximum principle” for -surfaces. Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (2007), no. 4, pp. 549–561DOI 10.1016/J.ANIHPC.2006.03.006