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

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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

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

Received July 2010 Revised April 2011 Published October 2011

Abstract
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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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