Published Paper

Inserted: 25 dec 2025
Last Updated: 31 dec 2025

Journal: J. Differential Equations
Year: 2020

Abstract:

We establish the higher differentiability of solutions to a class of obstacle problems for integral functionals where the convex integrand $f$ satisfies $p$-growth conditions with respect to the gradient variable. We derive that the higher differentiability property of the weak solution $v$ is related to the regularity of the assigned, under a suitable Sobolev assumption on the partial map that measures the oscillation of $f$ with respect to the $x$ variable. The main novelty is that such an assumption is independent of the dimension $n$ and that, in the case $p \le n-2$, it improves previous known results.