摘要
本文有四个目标:一是研究了H-Caccioppoli集的几何性质;二是证明了H^n上有界变差函数u的跳跃集J_u是H-Rectifiable并刻画不连续集S_u和跳跃集J_u的特征;三是证明了u在Ω上几乎处处近似可微并研究u的逐点行为;最后还证明了D_Hu作为Radon测度能分解成三部分,即D_Hu=L_u·^(2n+1)+2w_(2n-1)/w_(2n+1)(u^+-u^-)v_uS_d^(Q-1)J_u+_H^cu,其中L_u ∈ R^(2n)是u的近似微分,u^+,u^-,v_u分别是u在跳跃点的近似上、下极限和跳跃方向。
There are four goals: the first is to investigate some geometric properties of H-Cacciop-poli sets, the second is to prove that for u ∈ BVH(Ω) its jump set Ju is H-Rectifiable and to characterize discontinuity set Su and jump set Ju, the third is to prove that u ∈ BVH(Ω) is approximately differentiate a.e. in Ω and investigate pointwise behavior of u, while the last and the most important is to show that DHU as a Radon measure can be split into three parts. Namely, is the approximate differential of u, and u+, u-, vu are respectively the approximate upper limit, approximate lower limit and jump direction of u at a jump point.
出处
《数学年刊（A辑）》
CSCD
北大核心
2003年第5期541-554,共14页
Chinese Annals of Mathematics
基金
国家自然科学基金(No.19771048)
