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Sistemi ellittici di tipo A.D.N. a coefficienti variabili e condizioni di radiazione

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Summary

I study an elliptic system, in the sense of Agmon-Douglis-Nirenberg, of partial differential equations with variable coefficients. The matrix operator is of type P(D) + + λR(x, D) where λ εC, P(D) has constant coefficients, is elliptic, and his determinant admits a special elementary solution. On the coefficients in R(x, D), sufficiently smooth, a certain behaviour at the infinity is assumed. For suitable known vectors f, the problem P(D)u - λR(x, D)u=f is shown to be equivalent to a system of singular integral equations in special subspaces of [Wl,p]N, if N is the rank of the system, as is studied in [5]. This is possible when the unknown vector u belongs to a class that, generally, is stricter than the one of existence and uniquencess for P(D) [4]. Then results on the solvability of the system follow when λ is such that P(D+λR(x, D) is elliptic.

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Entrata in Redazione l'8 giugno 1977.

Lavoro svolto nell'ambito del « Laboratorio per la matematica applicata » del C.N.R. presso l'Università di Genova.

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Oppezzi, P. Sistemi ellittici di tipo A.D.N. a coefficienti variabili e condizioni di radiazione. Annali di Matematica 118, 143–161 (1978) doi:10.1007/BF02415127

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