On Iterations of the Green Integrals and their Applications to Elliptic Differential Complexes | Zendy

Nacinovich Mauro | Zendy; Shlapunov Alexandre | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

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.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research