Solvability of parabolic equations in divergence form with partially BMO coefficients |
| |
Authors: | Hongjie Dong |
| |
Institution: | Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912, USA |
| |
Abstract: | We prove the solvability of second order parabolic equations in divergence form with leading coefficients aij measurable in (t,x1) and having small BMO (bounded mean oscillation) semi-norms in the other variables. Additionally we assume a11 is measurable in x1 and has small BMO semi-norms in the other variables. The corresponding results for the Cauchy problem are also established. Parabolic equations in Sobolev spaces with mixed norms are also considered under the same conditions of the coefficients. |
| |
Keywords: | Second order equations Vanishing mean oscillation Partially BMO coefficients Sobolev spaces Mixed norms |
本文献已被 ScienceDirect 等数据库收录! |