### Abstract

We consider both divergence and non-divergence parabolic equations on a half space in weighted Sobolev spaces. All the leading coefficients are assumed to be only measurable in the time and one spatial variable except one coefficient, which is assumed to be only measurable either in the time or the spatial variable. As functions of the other variables the coefficients have small bounded mean oscillation (BMO) semi-norms. The lower-order coefficients are allowed to blow up near the boundary with a certain optimal growth condition. As a corollary, we also obtain the corresponding results for elliptic equations.

Original language | English |
---|---|

Pages (from-to) | 681-735 |

Number of pages | 55 |

Journal | Advances in Mathematics |

Volume | 274 |

DOIs | |

Publication status | Published - 2015 Apr 9 |

Externally published | Yes |

### Fingerprint

### Keywords

- Elliptic and parabolic equations
- Measurable coefficients
- Weighted Sobolev spaces

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Elliptic and parabolic equations with measurable coefficients in weighted Sobolev spaces.** / Dong, Hongjie; Kim, Doyoon.

Research output: Contribution to journal › Article

*Advances in Mathematics*, vol. 274, pp. 681-735. https://doi.org/10.1016/j.aim.2014.12.037

}

TY - JOUR

T1 - Elliptic and parabolic equations with measurable coefficients in weighted Sobolev spaces

AU - Dong, Hongjie

AU - Kim, Doyoon

PY - 2015/4/9

Y1 - 2015/4/9

N2 - We consider both divergence and non-divergence parabolic equations on a half space in weighted Sobolev spaces. All the leading coefficients are assumed to be only measurable in the time and one spatial variable except one coefficient, which is assumed to be only measurable either in the time or the spatial variable. As functions of the other variables the coefficients have small bounded mean oscillation (BMO) semi-norms. The lower-order coefficients are allowed to blow up near the boundary with a certain optimal growth condition. As a corollary, we also obtain the corresponding results for elliptic equations.

AB - We consider both divergence and non-divergence parabolic equations on a half space in weighted Sobolev spaces. All the leading coefficients are assumed to be only measurable in the time and one spatial variable except one coefficient, which is assumed to be only measurable either in the time or the spatial variable. As functions of the other variables the coefficients have small bounded mean oscillation (BMO) semi-norms. The lower-order coefficients are allowed to blow up near the boundary with a certain optimal growth condition. As a corollary, we also obtain the corresponding results for elliptic equations.

KW - Elliptic and parabolic equations

KW - Measurable coefficients

KW - Weighted Sobolev spaces

UR - http://www.scopus.com/inward/record.url?scp=84923039384&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84923039384&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2014.12.037

DO - 10.1016/j.aim.2014.12.037

M3 - Article

VL - 274

SP - 681

EP - 735

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -