Partial Differential Equations - Carleson estimates for the singular parabolic p-Laplacian in time-dependent domains, by Ugo Gianazza, communicated on 12 November 2021

We deal with the parabolic p-Laplacian in the so-called singular super-critical range 2N/N+1 < p < 2, and we prove Carleson estimates for non-negative solutions in suitable non-cylindrical domains Omega subset of RN+1. The sets Omega satisfy a proper NTA condition, tailored on the parabolic p-Laplacian. As an intermediate step, we show that in these domains non-negative solutions which vanish at the boundary, are Ho spacing diaeresis lder continuous up to the same boundary.