Methods and Applications of Analysis

Volume 16 (2009)

Number 3

Parabolic and Elliptic Systems with VMO Coefficients

Pages: 365 – 388

DOI: https://dx.doi.org/10.4310/MAA.2009.v16.n3.a6

Authors

Hongjie Dong

Doyoon Kim

Abstract

We consider second order parabolic and elliptic systems with leading coefficients having the property of vanishing mean oscillation (VMO) in the spatial variables. An $L_q − L_p$ theory is established for systems both in divergence and non-divergence form.

Keywords

Second order parabolic and elliptic systems, vanishing mean oscillation (VMO) coefficients, $L_q − L_p$ estimates, Sobolev spaces

2010 Mathematics Subject Classification

35D35, 35J47, 35K40, 35R05

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Published 1 January 2009