arXiv 0807.09262008-07math.AP

Second-order elliptic equations with variably partially VMO coefficients

N. V. Krylov

备注：: 17 pages. Auxiliary results slightly reorganized. Few misprints corrected

英文摘要：

The solvability in $W^{2}_{p}(\bR^{d})$ spaces is proved for second-order elliptic equations with coefficients which are measurable in one direction and VMO in the orthogonal directions in each small ball with the direction depending on the ball. This generalizes to a very large extent the case of equations with continuous or VMO coefficients.

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