Global Optimal Regularity for the Parabolic Polyharmonic Equations

Regularity theory in PDE plays an important role in the development of second-order elliptic and parabolic equations. Classical regularity estimates for elliptic and parabolic equations consist of Schauder estimates, L estimates, De Giorgi-Nash estimates, KrylovSafonov estimates, and so on. L and Schauder estimates, which play important roles in the theory of partial differential equations, are two fundamental estimates for elliptic and parabolic equations and the basis for the existence, uniqueness, and regularity of solutions. The objective of this paper is to investigate the generalization of L estimates, that is, regularity estimates in Orlicz spaces, for the following parabolic polyharmonic problems: