Global weighted estimates for the nonlinear parabolic equations with non-standard growth. (English) Zbl 1388.35110
Summary: In this paper we consider a nonlinear parabolic equation of \(p(x,t)\)-Laplacian type in divergence form with measurable data over non-smooth domains. We establish the global Calderón-Zygmund theory for the weak solutions of such a problem in the setting of weighted Lebesgue spaces. The nonlinearity of the coefficients is assumed to be discontinuous with respect to \((x,t)\)-variables and the lateral boundary of the domain is sufficiently flat beyond the Lipchitz category. As an application of the main result, the regularity in parabolic Morrey scales for the spatial gradient is also obtained.
MSC:
| 35K59 | Quasilinear parabolic equations |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35D30 | Weak solutions to PDEs |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 35R05 | PDEs with low regular coefficients and/or low regular data |
| 35R35 | Free boundary problems for PDEs |
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