NEUMANN PROBLEM FOR NON-DIVERGENCE ELLIPTIC AND PARABOLIC EQUATIONS WITH BMOx COEFFICIENTS IN WEIGHTED SOBOLEV SPACES

作者：Kim Doyoon; Dong Hongjie^*; Zhang Hong

来源：Discrete and Continuous Dynamical Systems, 2016, 36(9): 4895-4923.

DOI：10.3934/dcds.2016011

• L-p estimates
• weighted Sobolev spaces
• parabolic equations

We prove the unique solvability in weighted Sobolev spaces of non divergence form elliptic and parabolic equations on a half space with the homogeneous Neumann boundary condition. All the leading coefficients are assumed to be only measurable in the time variable and have small mean oscillations in the spatial variables. Our results can be applied to Neumann boundary value problems for stochastic partial differential equations with BMOx coefficients.

• 出版日期2016-9