非局部框架下的Helmholtz-Hodge分解。适定性分析及其应用
Helmholtz-Hodge decompositions in the nonlocal framework. Well-posedness analysis and applications
摘要：
出现在各种物理模型中的非定域算子满足恒等式，并具有与经典算子相似的一系列性质。在本文中，我们得到了Helmholtz-Hodge型分解的两点向量场的三个分量，有零非局部卷曲，零非局部发散，和第三个分量是（非局部）卷曲和发散自由。所得结果结合不同的非局部边界条件，从而适用于各种设置。
英文摘要：
Nonlocal operators that have appeared in a variety of physical models satisfy identities and enjoy a range of properties similar to their classical counterparts. In this paper we obtain Helmholtz-Hodge type decompositions for two-point vector fields in three components that have zero nonlocal curls, zero nonlocal divergence, and a third component which is (nonlocally) curl-free and divergence-free. The results obtained incorporate different nonlocal boundary conditions, thus being applicable in a variety of settings.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
