Boundary estimates for doubly nonlinear parabolic equations

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We consider non-negative, weak solutions to the doubly nonlinear parabolic equation ∂tuq-div|Du|p-2Du=0in the super-critical fast diffusion regime 0<p-1<q<N(p-1)(N-p)+. We show that when solutions vanish continuously at the Lipschitz boundary of a parabolic cylinder ΩT, they satisfy proper Carleson estimates. Assuming further regularity for the boundary of the domain ΩT, we obtain a power-like decay at the boundary and a boundary Harnack inequality.