TY - JOUR

T1 - Some space-time integrability estimates of the solution for heat equations in two dimensions

AU - Ioku, Norisuke

PY - 2011/9

Y1 - 2011/9

N2 - We study some space-time integrability estimates for a solution of an inhomogeneous heat equation in (0, T) × Ω with 0-Dirichlet boundary condition, where Ω is a bounded domain in ℝ2. We also discuss an exponential integrability estimate for the Poisson equation in Ω with 0-Dirichlet boundary condition.

AB - We study some space-time integrability estimates for a solution of an inhomogeneous heat equation in (0, T) × Ω with 0-Dirichlet boundary condition, where Ω is a bounded domain in ℝ2. We also discuss an exponential integrability estimate for the Poisson equation in Ω with 0-Dirichlet boundary condition.

KW - Brezis-Merle's inequality

KW - Lorentz-Zygmund spaces

UR - http://www.scopus.com/inward/record.url?scp=84878166908&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84878166908&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84878166908

SN - 1078-0947

SP - 707

EP - 716

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

IS - SUPPL.

ER -