Second-order elliptic equations with variably partially VMO coefficients

N. V. Krylov

Second-order elliptic equations with variably partially VMO coefficients

Analysis of PDEs 2008-10-29 v2

Authors: N. V. Krylov

Abstract

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.

Keywords

elliptic partial differential equations ordinary differential equations parabolic partial differential equations

Cite

@article{arxiv.0807.0926,
  title  = {Second-order elliptic equations with variably partially VMO coefficients},
  author = {N. V. Krylov},
  journal= {arXiv preprint arXiv:0807.0926},
  year   = {2008}
}

Comments

17 pages. Auxiliary results slightly reorganized. Few misprints corrected

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