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

Norisuke Ioku

doi:10.3934/proc.2011.2011.707

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2011, Volume 2011: 707-716. Doi: 10.3934/proc.2011.2011.707 open access

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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

Received: June 30, 2010

Revised: March 31, 2011

Published: August 2017

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Abstract

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.

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