### Abstract

We prove the W_{p}
^{1,2}-estimate and solvability for the Dirichlet problem of second-order parabolic equations in simple convex polytopes with time irregular coefficients, when p ∈ (1, 2]. We also consider the corresponding Neumann problem in a half space when p ∈ [2, ∞). Similar results are obtained for equations in a half space with coefficients which are measurable in a tangential direction and have small mean oscillations in the other directions. Equations with discontinuous coefficients in nonsmooth domains emerge from problems in mechanics, engineering, and biology, to name a few fields.

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

Pages (from-to) | 1789-1819 |

Number of pages | 31 |

Journal | SIAM Journal on Mathematical Analysis |

Volume | 46 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2014 Jan 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Boundary value problems
- Measurable coefficients
- Second-order parabolic equations
- Simple convex polytopes

### ASJC Scopus subject areas

- Analysis
- Computational Mathematics
- Applied Mathematics

### Cite this

**Parabolic equations in simple convex polytopes with time irregular coefficients.** / Dong, Hongjie; Kim, Doyoon.

Research output: Contribution to journal › Article

*SIAM Journal on Mathematical Analysis*, vol. 46, no. 3, pp. 1789-1819. https://doi.org/10.1137/130936890

}

TY - JOUR

T1 - Parabolic equations in simple convex polytopes with time irregular coefficients

AU - Dong, Hongjie

AU - Kim, Doyoon

PY - 2014/1/1

Y1 - 2014/1/1

N2 - We prove the Wp 1,2-estimate and solvability for the Dirichlet problem of second-order parabolic equations in simple convex polytopes with time irregular coefficients, when p ∈ (1, 2]. We also consider the corresponding Neumann problem in a half space when p ∈ [2, ∞). Similar results are obtained for equations in a half space with coefficients which are measurable in a tangential direction and have small mean oscillations in the other directions. Equations with discontinuous coefficients in nonsmooth domains emerge from problems in mechanics, engineering, and biology, to name a few fields.

AB - We prove the Wp 1,2-estimate and solvability for the Dirichlet problem of second-order parabolic equations in simple convex polytopes with time irregular coefficients, when p ∈ (1, 2]. We also consider the corresponding Neumann problem in a half space when p ∈ [2, ∞). Similar results are obtained for equations in a half space with coefficients which are measurable in a tangential direction and have small mean oscillations in the other directions. Equations with discontinuous coefficients in nonsmooth domains emerge from problems in mechanics, engineering, and biology, to name a few fields.

KW - Boundary value problems

KW - Measurable coefficients

KW - Second-order parabolic equations

KW - Simple convex polytopes

UR - http://www.scopus.com/inward/record.url?scp=84987650340&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84987650340&partnerID=8YFLogxK

U2 - 10.1137/130936890

DO - 10.1137/130936890

M3 - Article

AN - SCOPUS:84987650340

VL - 46

SP - 1789

EP - 1819

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

SN - 0036-1410

IS - 3

ER -