Abstract
We prove the solvability in Sobolev spaces for both divergence and non-divergence form higher order parabolic and elliptic systems in the whole space, on a half space, and on a bounded domain. The leading coefficients are assumed to be merely measurable only in the time variable and have small mean oscillations with respect to the spatial variables in small balls or cylinders. For the proof, we develop a set of new techniques to produce mean oscillation estimates for systems on a half space.
| Original language | English |
|---|---|
| Pages (from-to) | 889-941 |
| Number of pages | 53 |
| Journal | Archive for Rational Mechanics and Analysis |
| Volume | 199 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2011 Jan 1 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Analysis
- Mathematics (miscellaneous)
- Mechanical Engineering
Cite this
On the Lp-Solvability of Higher Order Parabolic and Elliptic Systems with BMO Coefficients. / Dong, Hongjie; Kim, Doyoon.
In: Archive for Rational Mechanics and Analysis, Vol. 199, No. 3, 01.01.2011, p. 889-941.Research output: Contribution to journal › Article
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TY - JOUR
T1 - On the Lp-Solvability of Higher Order Parabolic and Elliptic Systems with BMO Coefficients
AU - Dong, Hongjie
AU - Kim, Doyoon
PY - 2011/1/1
Y1 - 2011/1/1
N2 - We prove the solvability in Sobolev spaces for both divergence and non-divergence form higher order parabolic and elliptic systems in the whole space, on a half space, and on a bounded domain. The leading coefficients are assumed to be merely measurable only in the time variable and have small mean oscillations with respect to the spatial variables in small balls or cylinders. For the proof, we develop a set of new techniques to produce mean oscillation estimates for systems on a half space.
AB - We prove the solvability in Sobolev spaces for both divergence and non-divergence form higher order parabolic and elliptic systems in the whole space, on a half space, and on a bounded domain. The leading coefficients are assumed to be merely measurable only in the time variable and have small mean oscillations with respect to the spatial variables in small balls or cylinders. For the proof, we develop a set of new techniques to produce mean oscillation estimates for systems on a half space.
UR - http://www.scopus.com/inward/record.url?scp=79951813420&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79951813420&partnerID=8YFLogxK
U2 - 10.1007/s00205-010-0345-3
DO - 10.1007/s00205-010-0345-3
M3 - Article
AN - SCOPUS:79951813420
VL - 199
SP - 889
EP - 941
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
SN - 0003-9527
IS - 3
ER -