In this talk, the lecturer reports the continuity of a spatial gradient of a weak solution to the elliptic or parabolic (1, p)-Laplace equation with p∈(1, ∞). The main problem is that this equation becomes no longer uniformly elliptic or parabolic on the facet, the degenerate region of a gradient. In particular, it seems difficult to prove some quantitative gradient continuity estimates, especially on the boundary of the facet. However, by showing improved regularity estimates for a gradient that is truncated near its facet, we can conclude the gradient continuity even across the facet, in a qualitative way.