Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-26T13:13:23.924Z Has data issue: false hasContentIssue false

Some Relationships Between Bers and Beltrami Systems and Linear Elliptic Systems of Partial Differential Equations

Published online by Cambridge University Press:  20 November 2018

W. V. Caldwell*
Affiliation:
University of Michigan, Flint College
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Much work has been done in the investigation of the properties of solutions of linear elliptic systems of partial differential equations. Among these systems, the class of Beltrami systems has been studied for many years and has been shown to be of fundamental importance. Another class, perhaps of equal importance, is the class defined by Bers (1), which the author has taken the liberty of calling Bers systems. Solutions of these systems will be called Beltrami and Bers functions respectively.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Bers, L., Theory of pseudo-analytic functions (New York, 1953).Google Scholar
2. Bers, L. and Nirenberg, L., On a representation theorem for linear ellipitic systems with discontinuous coefficients and its applications, Convegno Internazionale Sulle Equazioni Lineari Aile Dériva te Parziali, (Trieste, 25-28 Agosto, 1954).Google Scholar
3. Caldwell, W. V., Vector spaces of light interior functions, J. Math, and Mech., 12 (1963), 411428.Google Scholar
4. Carleman, T., Sur les systèmes linéaires aux dérivées partielles du premier ordre à deux variables, C. R. Acad. Sri., Paris, 197 (1933), 471474.Google Scholar
5. Gergen, J. J. and Dressel, F. G., Mapping for elliptic equations, Trans. Am. Math. Soc, 77 (1954), 151178.Google Scholar
6. Golomb, M. A., A note on linear vector spaces o﹜mappings with positive Jacobians, Proc. Amer. Math. Soc, 5 (1954), 536578.Google Scholar
7. Kakutani, S., On the family of pseudo-regidar functions, Tohoku Math. J., 44 (1938), 211212.Google Scholar
8. Stöilow, S., Leçons sur les principes topologiques de la théorie des fonctions analytiques (Paris, 1956).Google Scholar
9. Titus, C. J. and McLaughlin, J. E., A characterization of analytic functions, Proc. Amer. Math. Soc, 5 (1954), 348351.Google Scholar
10. Titus, C. J. and Young, G. S., A Jacobian condition for interiority, Michigan Math J., 1 (1952), 8993.Google Scholar