## Differential and Integral Equations

### Gradient estimates for the heat equation in the exterior domains under the Neumann boundary condition

Kazuhiro Ishige

#### Abstract

We consider the Cauchy-Neumann problem for the heat equation in the exterior domain $\Omega$ of a compact set in ${\bf R}^N$ ($N\ge 2$). In this paper we give an estimate of the $L^\infty$-norm of the gradient of the solutions.

#### Article information

Source
Differential Integral Equations, Volume 22, Number 5/6 (2009), 401-410.

Dates
First available in Project Euclid: 20 December 2012