Global Optimal Regularity for the Parabolic Polyharmonic Equations. (14th June 2010) - Yao Yao, Fengping Fengping
Abstract : We show the global regularity estimates for the following parabolic polyharmonic equation u t + ( − Δ ) m u = f in ℝ n × ( 0, ∞ ), m ∈ ℤ + under proper conditions. Moreover, it will be verified that these conditions are necessary for the simplest heat equation u t − Δ u = f in ℝ n × ( 0, ∞ ) .