## Differential and Integral Equations

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

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

#### 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

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1356012873

**Mathematical Reviews number (MathSciNet)**

MR2866008

**Zentralblatt MATH identifier**

1249.35129

**Subjects**

Primary: 35K05: Heat equation 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

#### Citation

Ioku, Norisuke. Brezis-Merle type inequality for a heat equation in two dimensions. Differential Integral Equations 24 (2011), no. 11/12, 1021--1036. https://projecteuclid.org/euclid.die/1356012873