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2011, 2011(Special): 707-716. doi: 10.3934/proc.2011.2011.707

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

Norisuke Ioku 1,

1. 

Mathematical Institute, Tohoku University, Aoba 6-3, Aobaku, Sendai, 980-8578, Japan

Received  July 2010 Revised  April 2011 Published  October 2011

We study some space-time integrability estimates for a solution of an inhomogeneous heat equation in $(0,T) \times \Omega$ with 0-Dirichlet boundary condition, where $\Omega$ is a bounded domain in $\mathbb{R}^2$. We also discuss an exponential integrability estimate for the Poisson equation in $\Omega$ with 0-Dirichlet boundary condition.
Keywords: Lorentz-Zygmund spaces, Brezis-Merle's inequality.
Mathematics Subject Classification: Primary:35K05, Secondary:46E30.
Citation: Norisuke Ioku. Some space-time integrability estimates of the solution for heat equations in two dimensions. Conference Publications, 2011, 2011 (Special) : 707-716. doi: 10.3934/proc.2011.2011.707
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