Hölder regularity of solutions of degenerate elliptic and parabolic equations

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.