On homogenization problems with oscillating Dirichlet conditions in space–time domains

We prove the homogenization of fully nonlinear parabolic equations with periodic oscillating Dirichlet boundary conditions on certain general prescribed space–time domains. It was proved in (Feldman, J. Math. Pures Appl. 101 (2014), no. 5, 599–622; Feldman and Kim, Ann. Sci. Éc. Norm. Supér 50 (2017), 4, 1017–1064) that for elliptic equations, homogenized data exist at points irrational normal directions, it is generically discontinuous elsewhere. However, problems, a flat moving part boundary, we existence continuous g ¯ $\bar{g}$ . also show that, unlike case, can be even if operator rotation/reflection invariant.