Partial regularity of minimizers of asymptotically convex functionals with -growth
Volume 264 / 2022
Studia Mathematica 264 (2022), 71-102
MSC: Primary 46E35, 49N60; Secondary 35B65.
DOI: 10.4064/sm210104-20-9
Published online: 17 January 2022
Abstract
We consider vectorial minimizers of the integral functional \int _{\Omega }f(x,u,Du)\, dx, where the function (x,u,\xi )\mapsto f(x,u,\xi ) is asymptotically related to a simpler function (x,u,\xi )\mapsto a(x,u)|\xi |^{p(x)}. Thus, we consider asymptotically convex integral functionals in the p(x)-growth setting. We demonstrate that minimizers are almost everywhere Hölder continuous, in a manner that mimics that simpler p-growth setting.
