非齐次散度型椭圆方程的正则性

Regularity of Nonhomogeneous Divergence Elliptic Equation

从弱解的概念出发,经过推理计算,讨论了椭圆方程-div(A▽u)+b▽u+Vu=f弱解的一阶导数和二阶导数的积分估计,其中V,V2,|b|2∈Kato(Ω),f∈L2(Ω),从而推广了目前已有的结果.

Based on the definition of the weak solution, through inference and calculating, we mainly consider the integral estimation of the elliptic equation’s weak solution in this paper. The elliptic equation takes such a form as -div（A▽u）＋ b▽u＋Vu = f,where V,V2,｜b｜2∈Kato（Ω）,f∈L2（Ω）.The work in this paper extends the results previously published.