Abstract :
We establish the Alexandroff–Bakelman–Pucci estimate, the Harnack inequality, and the Hölder continuity of solutions to degenerate parabolic equations of the non-divergence form (∗)Lu≔xa11uxx+2xa12uxy+a22uyy+b1ux+b2uy−ut=gon x⩾0, with bounded measurable coefficients. We also establish similar regularity results in the corresponding elliptic case.
