再论蜕化抛物型方程的Harnack不等式  

Further discussion on the Harnack inequality for some degenerate parabolic equations

作　　者：黄清龙[1] Huang Qinglong(School of Mathematics and Physics, Changzhou University, C hangzhou 213164, China)

机构地区：[1]常州大学数理学院,江苏常州213164

出　　处：《湖南科技大学学报（自然科学版）》2016年第4期102-107,共6页Journal of Hunan University of Science And Technology：Natural Science Edition

基　　金：江苏省靖江市科技局与常州大学产学研合作项目(CDHJZ1509008)

摘　　要：讨论n维变系数二阶线性蜕化抛物型方程,在蜕化条件下利用抛物极值原理和不等式估计获得了该类抛物型微分方程的非负强解的Harnack性质.这一结论把一致抛物型方程的Harnack不等式推广到了一类新的蜕化抛物型微分方程,且所获Harnack不等式还可借助于三维抛物型微分方程的热传导性得以解释.Some n-dimensional variable coefficient linear second order degenerate parabolic equations were discussed. Under certain degeneration conditions, the Harnack property for nonnegative strong solution of degenerate parabolic equations was obtained by parabolic maximum principle and inequality estimates. The obtained conclusion extended the Harnack inequality for uniformly parabolic equations to a class of degenerate parabolic equations. An interpretation was given to this Harnack inequality in terms of heat conduction property of three-dimensional parabolic equations.

关 键 词：抛物型方程 蜕化 HARNACK不等式 热传导性 

分 类 号：O175.2[理学—数学]