Second-order elliptic equations with variably partially VMO coefficients

Details Second-order elliptic equations with variably partially VMO coefficients Second-order elliptic equations with variably partially VMO coefficients

2008-07-06

arxiv.org/abs/0807.0926v2

Mathematics

Analysis of PDEs

17 pages. Auxiliary results slightly reorganized. Few misprints corrected

Scientific paper

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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