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Research Article | Open Access

Optimal gradient estimates for multi-phase integrals

Dipartimento di Matematica "Giuseppe Peano", Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy
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Abstract

We prove sharp reverse Hölder inequalities for minima of multi-phase variational integrals and apply them to Calderón-Zygmund estimates for nonhomogeneous problems.

Keywords

regularitynonuniform ellipticitymulti-phase problems

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Mathematics in Engineering
Volume 4 Issue 5,
October 2022
Pages 1-36
DOI: 10.3934/mine.2022043

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De Filippis C. Optimal gradient estimates for multi-phase integrals. Mathematics in Engineering, 2022, 4(5): 1-36. https://doi.org/10.3934/mine.2022043

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Received: 01 July 2021
Accepted: 04 October 2021
Published: 15 October 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)