Neumann problem for non-divergence elliptic and parabolic equations with BMO$_x$ coefficients in weighted Sobolev spaces

Doyoon  Kim; Hongjie Dong; Hong  Zhang

doi:10.3934/dcds.2016011

Article Contents

2016, Volume 36, Issue 9: 4895-4914. Doi: 10.3934/dcds.2016011

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Neumann problem for non-divergence elliptic and parabolic equations with BMO$_x$ coefficients in weighted Sobolev spaces

1.
Department of Mathematics, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul, 02841
2.
Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912

Received: May 2015

Revised: February 2016

Published: May 2017

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Abstract

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 BMO$_x$ coefficients.

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Mathematics Subject Classification: Primary: 35J25, 35K20; Secondary: 35R05.

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References

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