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