Regularity results for solutions to obstacle problems with Sobolev coeffcients
Analysis of PDEs
2023-05-25 v1
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 assumption is independent of the dimension n and that, in the case p<=n-2, improves previous known results.
Keywords
Cite
@article{arxiv.1910.04506,
title = {Regularity results for solutions to obstacle problems with Sobolev coeffcients},
author = {Michele Caselli and Andrea Gentile and Raffaella Giova},
journal= {arXiv preprint arXiv:1910.04506},
year = {2023}
}