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arXiv · 1910.04506

Regularity results for solutions to obstacle problems with Sobolev coeffcients

Michele Caselli·Andrea Gentile·Raffaella Giova
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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.

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Michele Caselli, Andrea Gentile, Raffaella Giova. 2019-10-10. Regularity results for solutions to obstacle problems with Sobolev coeffcients. https://doi.org/10.1016/j.jde.2020.06.015

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