带有低阶项的非散度椭圆方程解的二阶导数的高阶可积性(英文)

Higher integrability result for solutions to nondivergence elliptic equations with low-order terms

研究如下形式的非散度椭圆方程解的二阶导数的高阶可积性,其中系数aij(x)有界且具有小BMO范数,bi(x),c(x)∈Ln(Ω),Ω为Rn(n≥3)中的有界光滑域.

We establish a higher integrability for second derivatives of solutions to the nondivergence elliptic equations of the following type Lu=∑n i,j=1 δij（x） δ^2u/δxiδxj＋∑n i=1bj（x）δu/δxi＋c（x）u=h（x） where the coefficients aij（x） are bounded and have small BMO-norm, and bi（x） and c（x） belong to L^n （Ω） where Ω is a bounded smooth domain in R^n （ n ≥ 3 ）.