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 -