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Generalized inverses of elliptic systems of differential operators with constant coefficients and related REDUCE programs for explicit calculations. (English) Zbl 0651.35027

Geometry and physics, Proc. Winter Sch., SrnĂ­/Czech. 1987, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 16, 21-28 (1987).
[For the entire collection see Zbl 0634.00015.]
Authors’ summary: It is shown how the theory of generalized inverses for closed densely defined linear operators \({\mathcal L}: H_ 1\to H_ 2\), \(H_ 1\) and \(H_ 2\) being Hilbert spaces, may be applied to the case where \({\mathcal L}={\mathcal L}(D)\) is an elliptic matrix differential operator with constant coefficients. For \({\mathcal L}(D)\) the gradient operator in \({\mathbb{R}}^ 3\) an example is worked out and the explicit solution is constructed by means of a REDUCE program.

MSC:

35J30 Higher-order elliptic equations
65Z05 Applications to the sciences
15A09 Theory of matrix inversion and generalized inverses
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)

Citations:

Zbl 0634.00015
Full Text: EuDML