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arXiv · 2008.08552

A simple proof of the generalized Leibniz rule on bounded Euclidean domains

Quoc-Hung Nguyen·Yannick Sire·Juan-Luis Vazquez
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Abstract

This note is devoted to a simple proof of the generalized Leibniz rule in bounded domains. The operators under consideration are the so-called spectral Laplacian and the restricted Laplacian. Equations involving such operators have been lately considered by Constantin and Ignatova in the framework of the SQG equation \cite{CI} in bounded domains and by two of the authors \cite{HungJuan} in the framework of the porous medium with nonlocal pressure in bounded domains. We will use the estimates in this work in a forthcoming paper on the study of Porous Medium Equations with pressure given by Riesz-type potentials .

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Quoc-Hung Nguyen, Yannick Sire, Juan-Luis Vazquez. 2020-08-19. A simple proof of the generalized Leibniz rule on bounded Euclidean domains. https://arxiv.org/abs/2008.08552

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