caa a22 4500 445843446 CHVBK 20180317145351.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s00526-010-0344-0 doi (NATIONALLICENCE)springer-10.1007/s00526-010-0344-0 L p solvability of divergence type parabolic and elliptic systems with partially BMO coefficients [Elektronische Daten] [Hongjie Dong, Doyoon Kim] We prove the $${{\mathcal{H}}^{1}_{p,q}}$$ solvability of second order systems in divergence form with leading coefficients A αβ only measurable in (t, x 1) and having small BMO (bounded mean oscillation) semi-norms in the other variables. In addition, we assume one of the following conditions is satisfied: (i) A 11 is measurable in t and has a small BMO semi-norm in the other variables; (ii) A 11 is measurable in x 1 and has a small BMO semi-norm in the other variables. The corresponding results for the Cauchy problem and elliptic systems are also established. Some of our results are new even for scalar equations. Using the results for systems in the whole space, we obtain the solvability of systems on a half space and Lipschitz domain with either the Dirichlet boundary condition or the conormal derivative boundary condition. Springer-Verlag, 2010 Dong Hongjie Division of Applied Mathematics, Brown University, 182 George Street, 02912, Providence, RI, USA aut Kim Doyoon Department of Applied Mathematics, Kyung Hee University, 1 Seochun-dong, Gihung-gu, 446-701, Yongin-si, Gyeonggi-do, Korea aut Calculus of Variations and Partial Differential Equations Springer-Verlag 40/3-4(2011-03-01), 357-389 0944-2669 40:3-4<357 2011 40 526 https://doi.org/10.1007/s00526-010-0344-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00526-010-0344-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dong Hongjie Division of Applied Mathematics, Brown University, 182 George Street, 02912, Providence, RI, USA aut NATIONALLICENCE 700 1- Kim Doyoon Department of Applied Mathematics, Kyung Hee University, 1 Seochun-dong, Gihung-gu, 446-701, Yongin-si, Gyeonggi-do, Korea aut NATIONALLICENCE 773 0- Calculus of Variations and Partial Differential Equations Springer-Verlag 40/3-4(2011-03-01), 357-389 0944-2669 40:3-4<357 2011 40 526 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer