## 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., Srní/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.)

Zbl 0634.00015
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