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In this paper we establish a local higher integrability result for the spatial gradient of weak solutions to doubly nonlinear parabolic systems. The proof is based on a new intrinsic scaling that involves both the solution and its spatial gradient. It allows to compensate for the different scaling of the system in |u| and |Du|. The result covers the range of parameters p > 2 n n + 2 and 0 < q ≤ 1 . © The Author(s) 2022.


Verena Bögelein, Frank Duzaar, Christoph Scheven. Higher integrability for doubly nonlinear parabolic systems. SN partial differential equations and applications. 2022;3(6):74

PMID: 36275331

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