一类具不同权函数的线性退化椭圆方程弱解的Hlder连续性  

Hlder Continuity of Weak Solutions for a Class of Degenerate Linear Elliptic Equations with Two Different Weights

作　　者：崔学伟[1] 

机构地区：[1]西北工业大学应用数学系,陕西西安710072

出　　处：《应用数学》2010年第3期531-538,共8页Mathematica Applicata

基　　金：国家自然科学基金资助项目(10871157);高等学校博士学科点专项科研基金(200806990032);西北工业大学科技创新基金资助项目(2007KJ01012,2008KJ02033)

摘　　要：本文研究了如下退化椭圆方程-∑ni,j=1Di(aij(x)Dju+diu)+∑ni=1biDiu+eu=f-∑ni=1Difi在具不同权函数下弱解的正则性.在方程低阶项系数属于退化Morrey空间的假定下,利用加权Sobolev不等式,退化Morrey空间的加权嵌入引理和经典的Mose迭代方法,证明了方程的弱解是局部有界的,获得了非负弱解的Harnack不等式,得到了方程弱解的Hlder连续性.A class of degenerate linear elliptic equations with different weights of the form-∑ni,j=1Di（aij（x）Dju＋diu）＋∑ni=1biDiu＋eu=f-∑ni=1Difiis studied.By weighted Sobolev inequality,weighted embedding lemma related to degenerate Morrey space and classic Moser＇s iteration method,local boundedness of weak solution and Harnack＇s inequality for nonnegative weak solution are proved under the assumption that the coefficients of the lower order terms are in degenerate Morrey space.As a consequence,local Hlder continuity of weak solution is obtained.

关 键 词：退化Morrey空间 权函数 HARNACK不等式 HOLDER连续性 

分 类 号：O175.25[理学—数学]