L~p-REGULARITY AND HOLDER CONTINUITY FOR SOLUTIONS OF SECOND ORDER PARABOLIC SYSTEMS

摘要

Under both controllable and natural growth conditions, the spatial derivatives D_auof a solution u∈ L2（0, T; H1（Q , RN）） ∩L∞（0, T; L2（Q , RN）） （or∩L∞（Q , RN）） of a nonlinearparabolic system u_ti - D_αA_iα（x, t, u, Du） = B_i（x, t, u, Du）, i = 1,…, N, （x, t） ∈Q,in fact, belong to L_locp（Q,RN） for some p2. Every solution of a quasilinear parabolic system u_ti - D_α[A_ijαβ（x, t, u）D_βuj +α_iα（x, t, u）] = B_i（x, t, u, Du）, i = 1, …, Nis Holder continuous in an open set Q₁?Q with Hn+2-p（QQ₁）=0. If A_ijαβ（x,t,u）=0 when ji, and the growth of B_i（x, t, u, p） w. r. t. |p| is less than 2, then Q₁=Q. If A_ijαβ and α_iαare Holder continuous, then so are D_αu in Q₁.