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.
Citation
Norisuke Ioku. "Brezis-Merle type inequality for a heat equation in two dimensions." Differential Integral Equations 24 (11/12) 1021 - 1036, November/December 2011. https://doi.org/10.57262/die/1356012873
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