The L regularity problem for elliptic equations satisfying a Carleson measure condition
نویسندگان
چکیده
We prove that the L2 regularity problem is solvable for the elliptic equation ∑n j,k=1 ∂j(ajk∂ku) = 0 when ∑ i,j,k |∂iajk(x)|xndx is a Carleson measure with a sufficiently small constant, ∑ i,j,k |∂iajk(x)| ≤ C/xn and the bottom row of the coefficient matrix has the particular form (0, 0, . . . , 0, 1). This is done in any dimension n. This was proved in the case n = 2 earlier in [9] without the assumption on the bottom row of (ajk).
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