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Helmholtz-Hodge decompositions in the nonlocal framework. Well-posedness analysis and applications

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 نشر من قبل Marta D'Elia
 تاريخ النشر 2019
  مجال البحث
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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.



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