Uniformly degenerate equations appear in many geometric and probabilistic problems and have been extensively studied. First, we present a concise overview of the optimal regularity of solutions to uniformly degenerate elliptic equations in bounded domains, and then discuss the decomposition of solutions near the boundary. Second, we explore the global H\older regularity and convergence of solutions to uniformly degenerate parabolic equations. This talk is based on joint work with Prof. Qing Han.
