Lp-REGULARITY AND HOLDER CONTINUITY FOR SOLUTIONS OF SECOND ORDER PARABOLIC SYSTEMS

被引：0
作者：
严子谦
机构：
[1] Changchun
[2] Jilin University
来源：
Science China Mathematics | 1989年 / 02期
关键词：
parabolic systems; systems of triangular form; regularity; nonlinear analysis;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Under both controllable and natural growth conditions, the spatial derivatives Duof a solution u∈ L(0, T; H（Q , R）) ∩L(0, T; L（Q , R）) (or∩L（Q , R）) of a nonlinearparabolic system u- DA（x, t, u, Du） = B（x, t, u, Du）, i = 1,…, N, （x, t） ∈Q,in fact, belong to L（Q,R） for some p>2. Every solution of a quasilinear parabolic system u- D[A（x, t, u）Du+α（x, t, u）] = B（x, t, u, Du）, i = 1, …, Nis Holder continuous in an open set Q?Q with H（QQ）=0. If A（x,t,u）=0 when j>i, and the growth of B（x, t, u, p） w. r. t. |p| is less than 2, then Q=Q. If Aand αare Holder continuous, then so are Du in Q.
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页码：154 / 167
页数：14
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