Calculus of Variations and Geometric Measure Theory

M. Carozza - A. Passarelli di Napoli - T. Schmidt - A. Verde

Local and asymptotic regularity results for quasiconvex and quasimonotone problems

created by schmidt on 22 Feb 2012
modified on 31 May 2012


Published Paper

Inserted: 22 feb 2012
Last Updated: 31 may 2012

Journal: Q. J. Math.
Volume: 63
Number: 2
Pages: 325-352
Year: 2012
Links: Link to the published version


Considering vectorial integrals in the multidimensional calculus of variations and quasilinear elliptic systems of partial differential equations, we prove gradient regularity of minimizers and weak solutions, respectively. In contrast to the classical theory, we impose our assumptions on the structure functions only locally (i.e. near a single point) or asymptotically (i.e. near infinity). In particular, we point out relations between the local and the asymptotic point of view, and we discuss notions of quasiconvexity at infinity and quasimonotonicity at infinity, which arise in this context.