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On Iterations of the Green Integrals and their Applications to Elliptic Differential Complexes
Author(s) -
Nacinovich Mauro,
Shlapunov Alexandre
Publication year - 1996
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.3211800111
Subject(s) - mathematics , sobolev space , overdetermined system , elliptic partial differential equation , mathematical analysis , order (exchange) , pure mathematics , corollary , elliptic operator , convergence (economics) , differential equation , finance , economics , economic growth
Convergence of iterations of special Green integrals for overdetermined elliptic linear partial differential operators P of order p ≥ 1 is proved. Using this result we obtain necessary and sufficient conditions for the solvability of the equation Pu = f in the Sobolev space W p , 2 (D) and, as a corollary, necessary and sufficient conditions for the vanishing of the first cohomology group of elliptic differential complexes. Also a criterion for the solvability of a P ‐Neumann problem for elliptic differential operators is proved.