Parabolic and elliptic systems in divergence form with variably partially BMO coefficients
Analysis of PDEs
2011-03-01 v3
Abstract
We establish the solvability of second order divergence type parabolic systems in Sobolev spaces. The leading coefficients are assumed to be only measurable in one spatial direction on each small parabolic cylinder with the spatial direction allowed to depend on the cylinder. In the other orthogonal directions and the time variable the coefficients have locally small mean oscillations. We also obtain the corresponding -solvability of second order elliptic systems in divergence form. Our results are new even for scalar equations and the proofs simplify the methods used previously in [12]
Keywords
Cite
@article{arxiv.0902.0390,
title = {Parabolic and elliptic systems in divergence form with variably partially BMO coefficients},
author = {Hongjie Dong and Doyoon Kim},
journal= {arXiv preprint arXiv:0902.0390},
year = {2011}
}
Comments
minor revision with an application to elasticity systems, 23 pages, to appear in SIAM J. Math. Anal