Regularity of minimizers under limit growth conditions. (April 2017)

• Record Type: Journal Article
• Authors: Cupini, Giovanni; Marcellini, Paolo; Mascolo, Elvira
• Is Part Of: Nonlinear analysis. Volume 153(2017)
• Page Start: 294
• Page End: 310
• Publication Date: 2017-04
• Subjects: primary 49N60 -- secondary 35J60; Anisotropic growth condition -- Local boundedness -- Non-coercive functional; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.06.002
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: It is well known that an integral of the Calculus of Variations satisfying anisotropic growth conditions may have unbounded minimizers if the growth exponents are too far apart. Under sharp assumptions on the exponents we prove the local boundedness of minimizers of functionals with anisotropic p, q -growth, via the De Giorgi method. As a by-product, regularity of minimizers of some non coercive functionals is obtained by reduction to coercive ones.