Differential and Integral Equations

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

Norisuke Ioku

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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

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

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

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