考虑了一致抛物型算子L=∂t-∑ni,j=1∂i(ai,j(x)∂j)+V(x),其中势函数V(x)是Rn(n≥3)上的非负函数,并且属于反霍尔德类.得到了算子L的基本解的梯度估计,以及算子VL-1,V1/2▽L-1和V1/2L-1/2在加权Lp(Rn+1)空间和Morrey空间上的估计.
Abstract
The uniformly parabolic operator L=∂t-∑ni,j=1∂i(ai,j(x)∂j)+V(x) is considered in this paper, where the potential V(x) is a non-negative function on Rn(n≥3), and belongs to reverse Hölder class. The estimate for the gradient of the fundamental solution of the operator L is studied and several estimates for VL-1,V1/2▽L-1 and V1/2L-1/2 on weighted Lp(Rn+1) spaces and Morrey spaces are obtained under certain assumptions on ai,j, V and p.
关键词
一致抛物算子 /
基本解 /
反霍尔德类 /
加权Lp空间 /
Morrey空间
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Key words
uniformly parabolic operator /
fundamental solution /
reverse Hölder class /
weighted Lp space /
Morrey space
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参考文献
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脚注
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基金
国家自然科学基金资助项目(10881010,11161044)
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