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On some non-linear elliptic differential functional equations. (English) Zbl 0142.38102

Full Text: DOI
[1] Bonnessen, T. & Fenchel, W.,Theorie der konvexen Körper. Ergeb. Math. (Berlin) 1934. · Zbl 0008.07708
[2] Bers, L., John, F. & Schecter, M.,Partial differential equations. (New York) 1964, Part II, Chapter 5.
[3] Browder, F. E., Non-linear elliptic boundary value problems II.Trans. Amer. Math. Soc., 117 (1965), 530--550. · Zbl 0127.31903 · doi:10.1090/S0002-9947-1965-0173846-9
[4] de Giorgi, E., Sulla differenziabilità e l’analiticità delle estremali degli integrali multipli regolari.Mem. Accad. Sci. Torino, 3 (1957), 25--43. · Zbl 0084.31901
[5] Gilbarg, D., Boundary value problems for nonlinear elliptic equations inn variables.Symposium on Nonlinear Problems, Madison (Wisconsin) 1962.
[6] Hartman, P., On the bounded slope condition. To appear,Pacific J. Math. · Zbl 0149.32001
[7] Ladyzhenskaia, O. A. &Ural’tseva, N. N., Quasi-linear elliptic equations and variational problems with many independent variables.Uspehi Mat. Nauk, 16 (1961), 19--92; translated inRussian Math. Surveys, 16 (1961), 17--91.
[8] Leray, J. &Lions, J. L., Quelques résultats de Visik sur les problèmes elliptiques nonlinéaires par les méthodes de Minty-Browder.Bull. Soc. Math. France, 93 (1965), 97--107. · Zbl 0132.10502
[9] Lewy, H., Über die Methode der Differenzengleichungen zur Lösung von Variations-und Randwertproblemen.Math. Ann., 98 (1928), 107--124. · Zbl 53.0438.02 · doi:10.1007/BF01451583
[10] Minty, G. J., Monotone (non-linear) operators in Hilbert space.Duke Math. J., 29 (1962), 341--346. · Zbl 0111.31202 · doi:10.1215/S0012-7094-62-02933-2
[11] Miranda, M., Un teorema di esistenza e unicità per il problema dell’area minima inn variabili.Ann. Scuola Norm. Sup. Pisa, 19 (1965), 233--249. · Zbl 0137.08201
[12] Rado, T.,On the problem of Plateau. Ergeb. Math. (Berlin) 1933. · Zbl 0007.11804
[13] Serrin, T., Local behavior of solutions of quasi-linear equations.Acta Math., 111 (1964), 247--302. · Zbl 0128.09101 · doi:10.1007/BF02391014
[14] Stampacchia, G., On some regular multiple integral problems in the calculus of variations.Comm. Pure Appl. Math., 16 (1963), 383--421. · Zbl 0138.36903 · doi:10.1002/cpa.3160160403
[15] Stampacchia, G., Formes bilinéaires coercitives sur les ensembles convexes.C. R. Acad. Sci. Paris, 258 (1964), 4413--4416. · Zbl 0124.06401