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On the null-spaces of first-order elliptic partial differential operators in $ R{\bf\sp{n}}$


Author: Homer F. Walker
Journal: Proc. Amer. Math. Soc. 30 (1971), 278-286
MSC: Primary 35.44
DOI: https://doi.org/10.1090/S0002-9939-1971-0280864-7
MathSciNet review: 0280864
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Abstract: The objects to be studied are the null-spaces of linear first-order elliptic partial differential operators with domain $ {H_1}({R^n};{C^k})$ in $ {L_2}({R^n};{C^k})$, the first-order coefficients of which become constant and the zero-order coefficients of which vanish outside a compact set in $ {R^n}$. An example is given of an operator of this type which has a nontrivial null-space. It is shown that the dimension of the null-space of such an operator is finite for any number n of independent variables, and that this dimension is an upper-semicontinuous function of the operator in a certain sense.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0280864-7
Keywords: Null-spaces of first-order elliptic operators, perturbation of first-order elliptic operators
Article copyright: © Copyright 1971 American Mathematical Society

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