Lp Regularity of the dirichlet problem for elliptic equations with singular drift
Lp Regularity of the dirichlet problem for elliptic equations with singular drift
复制标题
奇异漂移椭圆方程狄利克雷问题的 Lp 正则性
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
C. Rios
中科院分区：
文献类型：
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作者：
C. Rios
设L_0和L_1是两个非散度型椭圆算子，系数为Al，漂移项为bl，l = 0，1，满足sup| Y −X| ≤ δ（X）2| A0（Y）− A1（Y）|2 + δ（X）2| b0（Y）− b1（Y）|2 δ（X）dX是Lipschitz域Rn+1，n ≥ 1中的Carleson测度（这里δ（X）= dist（X，））.若调和测度dωL0 ∈ A∞，则dωL1 ∈ A∞.这与文[8]中关于散度型算子的定理2.17类似。作为应用，一个新的逼近参数和已知结果，我们推广了文[10]中关于散度型算子的结果，同时得到了关于非散度型算子的全新结果.这些定理在任何情况下都是精确的。
Let L0 and L1 be two elliptic operators in nondivergence form, with coefficients Al and drift terms bl, l = 0, 1 satisfying sup |Y −X|≤ δ(X) 2 |A0 (Y ) − A1 (Y )| 2 + δ (X) 2 |b0 (Y ) − b1 (Y )| 2 δ (X) dX is a Carleson measure in a Lipschitz domain Ω ⊂ Rn+1 , n ≥ 1, (here δ (X) = dist (X, ∂Ω)). If the harmonic measure dωL0 ∈ A∞, then dωL1 ∈ A∞. This is an analog to Theorem 2.17 in [8] for divergence form operators. As an application of this, a new approximation argument and known results we are able to extend the results in [10] for divergence form operators while obtaining totally new results for nondivergence form operators. The theorems are sharp in all cases.