Calculus of Variations and Geometric Measure Theory

P. Bousquet - L. Brasco - C. Leone

Singular orthotropic functionals with nonstandard growth conditions

created by brasco on 15 Nov 2022
modified on 05 Sep 2023


Accepted Paper

Inserted: 15 nov 2022
Last Updated: 5 sep 2023

Journal: Rev. Mat. Iberoam.
Pages: 45
Year: 2022


We pursue the study of a model convex functional with orthotropic structure and nonstandard growth conditions, this time focusing on the sub-quadratic case. We prove that bounded local minimizers are locally Lipschitz. No restriction on the ratio between the highest and the lowest growth rates are needed. The result holds also in presence of a non-autonomous lower order term, under sharp integrability assumptions. Finally, we prove higher differentiability of bounded local minimizers, as well.

Keywords: Lipschitz regularity, Nonstandard growth conditions, Sobolev regularity, singular elliptic equations, orthotropic functionals