Exact relations for Green's functions in linear PDE and boundary field equalities: a generalization of conservation laws

Graeme W. Milton, Daniel Onofrei

Many physics problems have $J(x)=L(x)E(x)+h(x)$, source $h(x)$, fields $E$,$J$ satisfying differential constraints, symbolized by $E\in \mathcal{E}$,$J\in \mathcal{J}$ where $\mathcal{E}$,$\mathcal{J}$…