论文标题
非局部扩散问题的对称性
Symmetrization in nonlocal diffusion problems
论文作者
论文摘要
我们研究Talenti的类型对称属性，以解决线性固定和进化问题的解决方案。当通过集成核定义的非局部扩散替换由二阶差分差异操作员定义的通常的局部扩散时，我们的主要结果确定了问题解决方案与其对称版本之间的比较。使用近似论点，我们恢复了古典人才定理的结果。我们方法的一种新颖性是，我们通过使用Riesz的重新排列不平等，取代了Talenti证明中使用的度量几何工具，从而提供了一种替代性和更简单的证明，而不是Talenti的证据。
We study Talenti's type symmetrization properties for solutions of linear stationary and evolution problems. Our main result establishes the comparison in norm between the solution of a problem and its symmetric version when nonlocal diffusion defined through integrable kernels is replacing the usual local diffusion defined by a second order differential operator. Using an approximation argument, we recover, as a corollary of our results, the classical Talenti's theorem. A novelty of our approach is that we replace the measure geometric tools employed in Talenti's proof by the use of the Riesz's rearrangement inequality, giving thus an alternative and somehow simpler proof than Talenti's one.
