Partial Hölder regularity for asymptotically convex functionals with borderline double‐phase growth

Abstract We study partial Hölder regularity of the local minimizers with to the integral functional in a bounded domain for . Under the assumption of asymptotically convex to the borderline double‐phase functional where satisfies VMO in and is continuous in , respectively, and is a strongly log‐Hölder continuous function, we prove that the local minimizer of such a functional is locally Hölder continuous with an explicit Hölder exponent in an open set with for some small , where denotes ‐dimensional Hausdorff measure.