The Wiener condition for the regularity at a boundary point of a weak solution, well-known for elliptic and parabolic equations, is now extended to the second-order degenerate parabolic equations. Moreover, using a suitable generalization of the \(\Gamma\)-capacity, some estimates are given for the modulus of continuity at a regular boundary point and for the energy decay of the solution. The results are presented in the linear case, but the author claimes that they are also valid for nonlinear equations with quadratic growth in the spatial gradient.