Neumann problem for non-divergence elliptic and parabolic equations with BMOX coefficients in weighted sobolev spaces

Doyoon Kim; Hongjie Dong; Hong Zhang

doi:10.3934/dcds.2016011

Neumann problem for non-divergence elliptic and parabolic equations with BMO_X coefficients in weighted sobolev spaces

Doyoon Kim, Hongjie Dong, Hong Zhang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We prove the unique solvability in weighted Sobolev spaces of non-divergence form elliptic and parabolic equations on a half space with the homo-geneous Neumann boundary condition. All the leading coeffcients 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 coeffcients.

Original language	English
Pages (from-to)	4895-4914
Number of pages	20
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	36
Issue number	9
DOIs	https://doi.org/10.3934/dcds.2016011
Publication status	Published - 2016 Sept

Bibliographical note

Funding Information:
D. Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2014R1A1A2054865).

Keywords

Lp estimates
Parabolic equations
Weighted Sobolev spaces

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.3934/dcds.2016011

Cite this

@article{c77226c7a0e845f294e5265bfd9f455e,

title = "Neumann problem for non-divergence elliptic and parabolic equations with BMOX coefficients in weighted sobolev spaces",

abstract = "We prove the unique solvability in weighted Sobolev spaces of non-divergence form elliptic and parabolic equations on a half space with the homo-geneous Neumann boundary condition. All the leading coeffcients 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 coeffcients.",

keywords = "Lp estimates, Parabolic equations, Weighted Sobolev spaces",

author = "Doyoon Kim and Hongjie Dong and Hong Zhang",

note = "Funding Information: D. Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2014R1A1A2054865).",

year = "2016",

month = sep,

doi = "10.3934/dcds.2016011",

language = "English",

volume = "36",

pages = "4895--4914",

journal = "Discrete and Continuous Dynamical Systems- Series A",

issn = "1078-0947",

publisher = "Southwest Missouri State University",

number = "9",

}

TY - JOUR

T1 - Neumann problem for non-divergence elliptic and parabolic equations with BMOX coefficients in weighted sobolev spaces

AU - Kim, Doyoon

AU - Dong, Hongjie

AU - Zhang, Hong

N1 - Funding Information: D. Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2014R1A1A2054865).

PY - 2016/9

Y1 - 2016/9

N2 - We prove the unique solvability in weighted Sobolev spaces of non-divergence form elliptic and parabolic equations on a half space with the homo-geneous Neumann boundary condition. All the leading coeffcients 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 coeffcients.

AB - We prove the unique solvability in weighted Sobolev spaces of non-divergence form elliptic and parabolic equations on a half space with the homo-geneous Neumann boundary condition. All the leading coeffcients 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 coeffcients.

KW - Lp estimates

KW - Parabolic equations

KW - Weighted Sobolev spaces

UR - http://www.scopus.com/inward/record.url?scp=84969168149&partnerID=8YFLogxK

U2 - 10.3934/dcds.2016011

DO - 10.3934/dcds.2016011

M3 - Article

AN - SCOPUS:84969168149

SN - 1078-0947

VL - 36

SP - 4895

EP - 4914

JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 9

ER -