Zharinov, V. V.; Marchuk, N. G. Green’s formulas and bilinear conservation laws. (English. Russian original) Zbl 0623.47055 Math. Notes 40, 776-780 (1986); translation from Mat. Zametki 40, No. 4, 478-483 (1986). Let L and M be two linear differential operators of dimensions \(t\times g\) respectively \(t\times h\) and let \(L^*\) be the adjoint of L. One proves that a Green formula \[ (Lu,Mv)=\sum^{m}_{i=1}\partial_ iJ^ i[u,v] \] (where (Lu,Mv) and \(J^ i[u,v]\) are bilinear forms in u and v, u,v being regular vector functions) holds iff \(L^*M=0\). Different examples are shown. Reviewer: C.Badea-Simionescu Cited in 1 Document MSC: 47F05 General theory of partial differential operators Keywords:linear differential operators; Green formula; bilinear forms; regular vector functions PDFBibTeX XMLCite \textit{V. V. Zharinov} and \textit{N. G. Marchuk}, Math. Notes 40, 776--780 (1986; Zbl 0623.47055); translation from Mat. Zametki 40, No. 4, 478--483 (1986) Full Text: DOI References: [1] V. S. Vladimirov and V. V. Zharinov, ?Closed forms associated with linear differential operators,? Differents. Uravn.,16, No. 5, 845-867 (1980). · Zbl 0506.35015 [2] S. G. Mikhlin, Linear Partial Differential Equations [in Russian], Vysshaya Shkola, Moscow (1977). · Zbl 0378.45003 [3] N. G. Marchuk, ?A broad class of Green’s formulas and conservation laws,? Dokl. Akad. Nauk SSSR,285, No. 6, 1325-1328 (1985). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.