Abstract
One proves an analogue of Weyl's decomposition of an arbitrary function f into potential and solenoidal parts with respect to a first-order operator L that generalizes the divergence. The only constraint on the operator L, besides the natural smoothness of the coefficients, is the requirement of the ellipticity of the operator LL *.
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References
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Additional information
Translated from Problemy Matematicheskogo Analiza, No. 11, pp. 46–50, 1990.
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Osmolovskii, V.G. An analogue of Weyl's decomposition for first-order operators. J Math Sci 64, 1253–1256 (1993). https://doi.org/10.1007/BF01098018
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DOI: https://doi.org/10.1007/BF01098018