@article{AIHPC_1989__6_5_347_0,
author = {Schulz, Friedmar},
title = {Univalent solutions of elliptic systems of {Heinz-Lewy} type},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {347--361},
year = {1989},
publisher = {Gauthier-Villars},
volume = {6},
number = {5},
mrnumber = {1030855},
zbl = {0698.35055},
language = {en},
url = {https://www.numdam.org/item/AIHPC_1989__6_5_347_0/}
}
TY - JOUR AU - Schulz, Friedmar TI - Univalent solutions of elliptic systems of Heinz-Lewy type JO - Annales de l'I.H.P. Analyse non linéaire PY - 1989 SP - 347 EP - 361 VL - 6 IS - 5 PB - Gauthier-Villars UR - https://www.numdam.org/item/AIHPC_1989__6_5_347_0/ LA - en ID - AIHPC_1989__6_5_347_0 ER -
Schulz, Friedmar. Univalent solutions of elliptic systems of Heinz-Lewy type. Annales de l'I.H.P. Analyse non linéaire, Tome 6 (1989) no. 5, pp. 347-361. https://www.numdam.org/item/AIHPC_1989__6_5_347_0/
[1] , On Univalent Mappings by Solutions of Linear Elliptic Partial Differential Equations, Trans. Amer. Math. Soc., Vol. 84, 1957, pp. 310-318. | Zbl | MR
[2] , Equazioni Ellittiche del II0 Ordine e Spazi L(2,λ), Ann. Mat. Pura Appl., IV. Ser., Vol. 69, 1965, pp. 321-381. | Zbl | MR
[3] , Sistemi Ellittici in Forma Divergenza. Regolarità all'Interno. Quaderni, Scuola Normale Superiore, Pisa, 1980. | Zbl | MR
[4] , Sur les Systèmes Linéaires aux Dérivées Partielles du Premier Ordre à Deux Variables, C. R. Acad. Sci. Paris, Vol. 197, 1933, pp. 471-474. | Zbl | JFM
[5] , Multiple integrals in the calculus of variations and nonlinear elliptic systems, Ann. Math. Studies, Vol. 105, Princeton University Press, Princeton, N.J., 1983. | Zbl | MR
[6] , Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces, Interscience Publishers, New York, London, 1950. | Zbl | MR
[7] and , On the Local Behavior of Solutions of Non-Parabolic Partial Differential Equations, Am. J. Math., Vol. 75, 1953, pp. 449-476. | Zbl | MR
[8] , Über gewisse elliptische Systeme von Differentialgleichungen zweiter Ordnung mit Anwendung auf die Monge-Ampèresche Gleichung, Math. Ann., Vol. 131, 1956, pp. 411-428. | Zbl | MR
[9] , On Certain Nonlinear Elliptic Differential Equations and Univalent Mappings, J. Anal. Math., Vol. 5, 1956/1957, pp. 197-272. | Zbl | MR
[10] , On Elliptic Monge-Ampère Equations and Weyl's Embedding Problem, J. Anal. Math., Vol. 7, 1959, pp. 1-52. | Zbl | MR
[11] , Neue a-priori-Abschätzungen für den Ortsvektor einer Fläche positiver Gausscher Krümmung durch ihr Linienelement, Math. Z., Vol. 74, 1960, pp. 129- 157. | Zbl | MR
[12] , 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. | Zbl | MR
[13] , Existence Theorems for One-To-One Mappings Associated with Elliptic Systems of Second Order I, J. Anal. Math., Vol. 15, 1965, pp. 325-352. | Zbl | MR
[14] , Existence Theorems for One-To-One Mappings Associated with Elliptic Systems of Second Order II, J. Anal. Math., Vol. 17, 1966, pp. 145-184. | Zbl | MR
[15] , Über das Nichtverschwinden der Funktionaldeterminante bei einer Klasse eineindeutiger Abbildungen, Math. Z., Vol. 105, 1968, pp. 87-89. | Zbl | MR
[16] , A-priori-Abschätzungen für isometrische Einbettungen zweidimensionaler Riemannscher Mannigfaltigkeiten in drei-dimensionale Riemannsche Räume, Math. Z., Vol. 100, 1967, pp. 1-16. | Zbl | MR
[17] , Zur Abschätzung der Funktionaldeterminante bei einer Klasse topologischer Abbildungen, Nachr. Akad. Wiss. Göttingen, II. Math.-Phys. Kl., 1968, pp. 183-197. | Zbl | MR
[18] , Univalency of Harmonic Mappings Between Surfaces, J. Reine Angew. Math., Vol. 324, 1981, pp. 141-153. | Zbl | MR
[19] and , On the Existence of Harmonic Diffeomorphisms Between Surfaces, Invent. Math., Vol. 66, 1982, pp. 353-359. | Zbl | MR
[20] , On the Non-Vanishing of the Jacobian in Certain One-To-One Mappings, Bull. Am. Math. Soc., Vol. 42, 1936, pp. 689-692. | Zbl
[21] , A priori Limitations for Solutions of Monge-Ampère Equations. II, Trans. Am. Math. Soc., Vol. 41, 1937, pp. 365-374. | Zbl | MR
[22] , Regularity of Convex Surfaces (to appear). | MR






