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

Pages: 707 - 716, Issue Special, September 2011

 Abstract        Full Text (360.7K)              

Norisuke Ioku - Mathematical Institute, Tohoku University, Aoba 6-3, Aobaku, Sendai, 980-8578, Japan (email)

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

Received: July 2010;      Revised: April 2011;      Published: October 2011.