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

References:
[1]Bonnessen, T. & Fenchel, W.,Theorie der konvexen Körper. Ergeb. Math. (Berlin) 1934.
[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. · 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.
[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.
[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.
[9]Lewy, H., Über die Methode der Differenzengleichungen zur Lösung von Variations-und Randwertproblemen.Math. Ann., 98 (1928), 107–124. · Zbl 02582322 · 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.
[12]Rado, T.,On the problem of Plateau. Ergeb. Math. (Berlin) 1933.
[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.