Calculus of Variations and Geometric Measure Theory

G. Cupini - P. Marcellini - E. Mascolo

Regularity of minimizers under limit growth conditions

created by cupini on 14 Oct 2016


Accepted Paper

Inserted: 14 oct 2016
Last Updated: 14 oct 2016

Journal: Nonlinear Analysis
Year: 2016
Doi: 10.1016/


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.

Keywords: local boundedness, anisotropic growth condition, Non-coercive functional