کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6417297 | 1338685 | 2011 | 16 صفحه PDF | دانلود رایگان |
The local behavior of solutions to a degenerate elliptic equationdivA(x)âu=0inΩâRn where A(x)=At(x) andw(x)|ξ|2⩽ãA(x)ξ,ξã⩽v(x)|ξ|2 for weights w(x)⩾0 and v(x), has been studied by Chanillo and Wheeden. In Chanillo and Wheeden (1986) [7], they generalize the results of Fabes, Kenig, and Serapioni (1961) [8] relative to the case v(x)=Îw(x).We consider the case where w(x)=1K(x) and v(x)=K(x). The assumption that vâA2, the Muckenhoupt class, is not sufficient as it was in the case v(x)=Îw(x) to obtain the continuity of local solutions. However, if vâGn, the Gehring class, and if Sv is the domain of the maximal function of v,Sv={xâΩ:Mv(x)<â}, then the restriction to Sv of the precise̲ representative uË of any non-negative solution u is continuous.
Journal: Journal of Differential Equations - Volume 250, Issue 6, 15 March 2011, Pages 2671-2686