Regularity for nonlocal problems with non-standard growth

Abstract

We study robust regularity estimates for local minimizers of nonlocal functionals with non-standard growth of $(p,q)$-type and for weak solutions to a related class of nonlocal equations. The main results of this paper are local boundedness and Hölder continuity of minimizers and weak solutions. Our approach is based on the study of corresponding De Giorgi classes.

arXiv comment30 pages

References in corpus (6)

• Local behavior of fractional $p$-minimizers
• Regularity results and Harnack inequalities for minimizers and solutions of nonlocal problems: a unified approach via fractional De Giorgi classes
• Harnack inequality for nonlocal problems with non-standard growth
• Global regularity results for non-homogeneous growth fractional problems
• Interior and boundary regularity results for strongly nonhomogeneous $p,q$-fractional problems
• Local Hölder regularity for nonlocal equations with variable powers

Cited by in corpus (4)

• On the Obstacle Problem in Fractional Generalised Orlicz Spaces
• Wolff potential estimates and Wiener criterion for nonlocal equations with Orlicz growth
• Lower bounds for fractional Orlicz-type eigenvalues
• On the Stability of the $s$-Nonlocal $p$-Obstacle Problem and their Coincidence Sets and Free Boundaries