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arXiv · 2308.10222

Regularity for double phase problems at nearly linear growth

Cristiana De Filippis·Giuseppe Mingione
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Abstract

Minima of functionals of the type $$ w\mapsto \int_{\Omega}\left[\snr{Dw}\log(1+\snr{Dw})+a(x)\snr{Dw}^{q}\right] \dx\,, \quad 0\leq a(\cdot) \in C^{0, \alpha}\,,$$ with $\Omega \subset \er^n$, have locally H\"older continuous gradient provided $1 < q < 1+\alpha/n$.

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Cristiana De Filippis, Giuseppe Mingione. 2023-08-20. Regularity for double phase problems at nearly linear growth. https://doi.org/10.1007/s00205-023-01907-3

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