Self-improving property of nonlinear higher order parabolic systems near the boundary

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Higher integrability for parabolic systems with non-standard growth and degenerate diffusions (2011, background): “Finally, the case of higher order parabolic systems with degenerate diffusions was treated in [7], [11].”
Global weighted estimates for the gradient of solutions to nonlinear elliptic equations (2013, background): “We refer to [11,25,26] and references therein for a further discussion on local and global integrability of gradients in nonlinear problems.”
Global Calderón–Zygmund theory for nonlinear parabolic systems (2013, methodology): “The qualitative higher integrability result, i.e. Dv ∈ L p (1+ ε o ) ( Q + ̺/ 2 ,λ ( z o ) , R Nn ) directly follows from [29, 11], but the quantitative estimates are stated there only on standard cylinders, i.e. for the case λ = 1 .”