Higher integrability for parabolic systems with Orlicz growth

Abstract

We prove higher integrability of the spatial gradient of weak solutions to parabolic systems with $\varphi$-growth, where $\phi =\phi (t)$ 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.

References in corpus (2)

• Maximal regularity for local minimizers of non-autonomous functionals
• Higher integrability for doubly nonlinear parabolic systems

Cited by in corpus (1)

• Gradient estimates for parabolic problems with Orlicz growth and discontinuous coefficients