Higher integrability for doubly nonlinear parabolic systems. (English) Zbl 1501.35097
Summary: 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 \(p>\frac{2n}{n+2}\) and \(0<q\le 1\).
MSC:
| 35B45 | A priori estimates in context of PDEs |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35K40 | Second-order parabolic systems |
| 35K59 | Quasilinear parabolic equations |
| 35K92 | Quasilinear parabolic equations with \(p\)-Laplacian |
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