TY - JOUR

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

AU - Dong, Hongjie

AU - Kim, Doyoon

N1 - Funding Information:
This author was partially supported by the NSF under agreement DMS-1056737. This author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (2011-0013960).
Publisher Copyright:
© 2014 Society for Industrial and Applied Mathematics.

PY - 2014

Y1 - 2014

N2 - We prove the Wp1,2-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 Wp1,2-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

U2 - 10.1137/130936890

DO - 10.1137/130936890

M3 - Article

AN - SCOPUS:84987650340

SN - 0036-1410

VL - 46

SP - 1789

EP - 1819

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 3

ER -