Univalent solutions of elliptic systems of Heinz-Lewy type

 Access to full text

 Full (PDF)

1. [1] P.W. Berg, On Univalent Mappings by Solutions of Linear Elliptic Partial Differential Equations, Trans. Amer. Math. Soc., Vol. 84, 1957, pp. 310-318. Zbl0079.29901MR83657
2. [2] S. Campanato, Equazioni Ellittiche del II0 Ordine e Spazi L(2,λ), Ann. Mat. Pura Appl., IV. Ser., Vol. 69, 1965, pp. 321-381. Zbl0145.36603MR192168
3. [3] S. Campanato, Sistemi Ellittici in Forma Divergenza. Regolarità all'Interno. Quaderni, Scuola Normale Superiore, Pisa, 1980. Zbl0453.35026MR668196
4. [4] T. Carleman, Sur les Systèmes Linéaires aux Dérivées Partielles du Premier Ordre à Deux Variables, C. R. Acad. Sci. Paris, Vol. 197, 1933, pp. 471-474. Zbl0007.16202JFM59.0469.03
5. [5] M. Giaquinta, Multiple integrals in the calculus of variations and nonlinear elliptic systems, Ann. Math. Studies, Vol. 105, Princeton University Press, Princeton, N.J., 1983. Zbl0516.49003MR717034
6. [6] R. Courant, Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces, Interscience Publishers, New York, London, 1950. Zbl0040.34603MR36317
7. [7] P. Hartman and A. Wintner, On the Local Behavior of Solutions of Non-Parabolic Partial Differential Equations, Am. J. Math., Vol. 75, 1953, pp. 449-476. Zbl0052.32201MR58082
8. [8] E. Heinz, Über gewisse elliptische Systeme von Differentialgleichungen zweiter Ordnung mit Anwendung auf die Monge-Ampèresche Gleichung, Math. Ann., Vol. 131, 1956, pp. 411-428. Zbl0072.31103MR123809
9. [9] E. Heinz, On Certain Nonlinear Elliptic Differential Equations and Univalent Mappings, J. Anal. Math., Vol. 5, 1956/1957, pp. 197-272. Zbl0085.08701MR136852
10. [10] E. Heinz, On Elliptic Monge-Ampère Equations and Weyl's Embedding Problem, J. Anal. Math., Vol. 7, 1959, pp. 1-52. Zbl0152.30901MR111943
11. [11] E. Heinz, Neue a-priori-Abschätzungen für den Ortsvektor einer Fläche positiver Gausscher Krümmung durch ihr Linienelement, Math. Z., Vol. 74, 1960, pp. 129- 157. Zbl0096.36601MR116294
12. [12] E. Heinz, Interior Estimates for Solutions of Elliptic Monge-Ampère Equations, in Partial Differential Equations, Proceedings of Symposia in Pure Mathematics, Vol. IV, Berkeley, CA, 1960, pp. 149-155, American Mathematical Society, Providence, R.I., 1961. Zbl0192.20001MR157100
13. [13] E. Heinz, Existence Theorems for One-To-One Mappings Associated with Elliptic Systems of Second Order I, J. Anal. Math., Vol. 15, 1965, pp. 325-352. Zbl0137.07202MR183966
14. [14] E. Heinz, Existence Theorems for One-To-One Mappings Associated with Elliptic Systems of Second Order II, J. Anal. Math., Vol. 17, 1966, pp. 145-184. Zbl0144.14901MR217743
15. [15] E. Heinz, Über das Nichtverschwinden der Funktionaldeterminante bei einer Klasse eineindeutiger Abbildungen, Math. Z., Vol. 105, 1968, pp. 87-89. Zbl0159.40203MR226196
16. [16] E. Heinz, A-priori-Abschätzungen für isometrische Einbettungen zweidimensionaler Riemannscher Mannigfaltigkeiten in drei-dimensionale Riemannsche Räume, Math. Z., Vol. 100, 1967, pp. 1-16. Zbl0158.40105MR220222
17. [17] E. Heinz, Zur Abschätzung der Funktionaldeterminante bei einer Klasse topologischer Abbildungen, Nachr. Akad. Wiss. Göttingen, II. Math.-Phys. Kl., 1968, pp. 183-197. Zbl0165.44802MR246236
18. [18] J. Jost, Univalency of Harmonic Mappings Between Surfaces, J. Reine Angew. Math., Vol. 324, 1981, pp. 141-153. Zbl0453.53036MR614521
19. [19] J. Jost and R. Schoen, On the Existence of Harmonic Diffeomorphisms Between Surfaces, Invent. Math., Vol. 66, 1982, pp. 353-359. Zbl0488.58009MR656629
20. [20] H. Lewy, On the Non-Vanishing of the Jacobian in Certain One-To-One Mappings, Bull. Am. Math. Soc., Vol. 42, 1936, pp. 689-692. Zbl0015.15903
21. [21] H. Lewy, A priori Limitations for Solutions of Monge-Ampère Equations. II, Trans. Am. Math. Soc., Vol. 41, 1937, pp. 365-374. Zbl0017.21101MR1501906
22. [22] F. Schulz, Regularity of Convex Surfaces (to appear). MR80325