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arXiv · 2401.02186

Regularity for multi-phase problems at nearly linear growth

Filomena De Filippis·Mirco Piccinini
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Abstract

Minima of the log-multiphase variational integral $$ w \mapsto \int_{\Omega} \left[|Dw|\log(1+|Dw|) + a(x)|Dw|^q + b(x)|Dw|^s\right] \, {\rm d}x\,, $$ have locally H\"older continuous gradient under sharp quantitative bounds linking the growth powers $(q,s)$ to the H\"older exponents of the modulating coefficients $a(\cdot)$ and $b(\cdot)$ respectively.

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Filomena De Filippis, Mirco Piccinini. 2024-01-04. Regularity for multi-phase problems at nearly linear growth. https://doi.org/10.1016/j.jde.2024.08.023

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