Global Lp Estimates for the Parabolic Equation of the Bi-harmonic Type

Abstract

In this paper similarly to the second-order case, we give an elementary and straightforward proof of global L^p estimates for the initial-value parabolic problem of the bi-harmonic type. Moreover, we obtain the existence and uniqueness of the solutions in the suitable space using the potential theory, Marcinkiewicz interpolation theorem and approximation argument. Meanwhile, by the same approach we can deal with the general polyharmonic cases.