论文标题
对有限的欧几里得领域的广义莱布尼兹规则的简单证明
A simple proof of the generalized Leibniz rule on bounded Euclidean domains
论文作者
论文摘要
该注释专门用于有限域中的广义Leibniz规则的简单证明。所考虑的操作员是所谓的光谱拉普拉斯和受限制的拉普拉斯人。最近，康斯坦丁和Ignatova在有限域中的SQG方程\ CITE {CI}的框架中考虑了涉及此类运算符的方程，并在有限域中具有非局部压力的多孔介质的两个作者\ cite \ cite \ cite {hughjuan}。我们将在即将发表的有关Riesz型电势压力的多孔培养基方程的研究中使用这项工作的估计值。
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 .
