Second-order elliptic equations with variably partially VMO coefficients
Abstract
Description
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.
17 pages. Auxiliary results slightly reorganized. Few misprints corrected
17 pages. Auxiliary results slightly reorganized. Few misprints corrected