Peter Hästö, Jihoon Ok
Published 2019-05-14Version 1
We prove higher integrability of the spatial gradient of weak solutions to parabolic systems with $\phi$-growth, where $\varphi=\varphi(t)$ is a general Orlicz function. The parabolic systems need be neither degenerate nor singular. Our result is a generalized version of the one of J. Kinnunen and J. Lewis [Duke Math. J. 102 (2000), no. 2, 253--271] for the parabolic $p$-Laplace systems.
$\mathcal{A}$-caloric approximation and partial regularity for parabolic systems with Orlicz growth
Regularity theory for parabolic systems with Uhlenbeck structure
Regularity conditions for solutions to some parabolic systems
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