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.

引用

页码：154 / 167

页数：14

共 49 条

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