Differential and Integral Equations

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

Kazuhiro Ishige

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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

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019598

Mathematical Reviews number (MathSciNet)
MR2501676

Zentralblatt MATH identifier
1240.35215

Citation

Ishige, Kazuhiro. Gradient estimates for the heat equation in the exterior domains under the Neumann boundary condition. Differential Integral Equations 22 (2009), no. 5/6, 401--410. https://projecteuclid.org/euclid.die/1356019598.


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