Green functions for first order equations
Mathematics. Physics. Mechanics
Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
AbstractGreen functions for first order differential equations are considered rather than for common second order equations (for Poisson equation, e.g.). It is shown that a delta function for first order equations gives a closed part of the function that is integrated with the delta function rather than the original function itself as is common. A solution for a first order differential equation is considered as generating. Formulae are presented which relate the generating operator and a boundary operator. The Helmgoltz decomposition is compared with the Poincare decomposition.
Keywords:delta functions; field boundary; Hodge operation; Helmgoltz decomposition