Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
MathSciNet review: 0280864
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)

  • [1] L. Bers, F. John and M. Schecter, Partial differential equations, Lectures in Appl. Math., vol. 3, Interscience, New York, 1964. MR 29 #346.
  • [2] Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
  • [3] Peter D. Lax and Ralph S. Phillips, Scattering theory, Rocky Mountain J. Math. 1 (1971), no. 1, 173–223. MR 0412636
  • [4] Peter D. Lax and Ralph S. Phillips, Scattering theory, Pure and Applied Mathematics, Vol. 26, Academic Press, New York-London, 1967. MR 0217440

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35.44

Retrieve articles in all journals with MSC: 35.44


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