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Some space-time integrability estimates of the solution for heat equations in two dimensions

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  • We study some space-time integrability estimates for a solution of an inhomogeneous heat equation in $(0,T) \times \Omega$ with 0-Dirichlet boundary condition, where $\Omega$ is a bounded domain in $\mathbb{R}^2$. We also discuss an exponential integrability estimate for the Poisson equation in $\Omega$ with 0-Dirichlet boundary condition.
    Mathematics Subject Classification: Primary:35K05, Secondary:46E30.

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