## Differential and Integral Equations

### Brezis-Merle type inequality for a heat equation in two dimensions

Norisuke Ioku

#### Abstract

We consider the regularity estimate for the solution of the inhomogeneous heat equation in $(0,T)\times \Omega$ with 0-Dirichlet boundary conditions, where $\Omega$ is a bounded domain in $\mathbb{R}^2$. We choose the external force $f$ from the Lorentz-Zygmund space which is not a reflexive Banach space, therefore our estimate cannot be obtained by a simple application of the estimate of the maximal regularity.

#### Article information

Source
Differential Integral Equations, Volume 24, Number 11/12 (2011), 1021-1036.

Dates
First available in Project Euclid: 20 December 2012