Local and asymptotic regularity results for quasiconvex and quasimonotone problems

Carozza M, Passarelli di Napoli A, Schmidt T, Verde A (2012)

Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2012

Journal

Quarterly Journal of Mathematics Oxford University Press (OUP): Policy B

Publisher: Oxford University Press (OUP): Policy B

Book Volume: 63

Pages Range: 325-352

Journal Issue: 2

URI: http://cvgmt.sns.it/paper/1767/

DOI: 10.1093/qmath/haq044

Abstract

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. © 2010 Published by Oxford University Press. All rights reserved.

Authors with CRIS profile

Thomas Schmidt Department Mathematik

Involved external institutions

Università degli Studi del Sannio di Benevento IT Italy (IT) Università degli Studi di Napoli Federico II IT Italy (IT)

How to cite

APA:

Carozza, M., Passarelli di Napoli, A., Schmidt, T., & Verde, A. (2012). Local and asymptotic regularity results for quasiconvex and quasimonotone problems. Quarterly Journal of Mathematics, 63(2), 325-352. https://dx.doi.org/10.1093/qmath/haq044

MLA:

Carozza, Menita, et al. "Local and asymptotic regularity results for quasiconvex and quasimonotone problems." Quarterly Journal of Mathematics 63.2 (2012): 325-352.

BibTeX: Download