Optimal gradient estimates for multi-phase integrals

Cristiana De Filippis; Cristiana De Filippis

doi:10.3934/mine.2022043

Mathematics in Engineering

2022, Volume 4, Issue 5: 1-36. doi: 10.3934/mine.2022043

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Optimal gradient estimates for multi-phase integrals

Cristiana De Filippis ^,

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

Received: 01 July 2021 Accepted: 04 October 2021 Published: 25 October 2021

We prove sharp reverse Hölder inequalities for minima of multi-phase variational integrals and apply them to Calderón-Zygmund estimates for nonhomogeneous problems.
- regularity,
- nonuniform ellipticity,
- multi-phase problems
Citation: Cristiana De Filippis. Optimal gradient estimates for multi-phase integrals[J]. Mathematics in Engineering, 2022, 4(5): 1-36. doi: 10.3934/mine.2022043

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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.

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