Acta Mathematica

On some non-linear elliptic differential-functional equations

Philip Hartman and Guido Stampacchia

Full-text: Open access

Note

This research was partially supported by the Air Force Office of Scientific Research under Contract AF 49 (638)-1382 and Grant AF EOAR 65-42.

Note

This revised version was published online in November 2006 with corrections to the Cover Date.

Article information

Source
Acta Math. Volume 115 (1966), 271-310.

Dates
Received: 19 May 1965
Revised: 30 June 1965
First available in Project Euclid: 31 January 2017

Permanent link to this document
http://projecteuclid.org/euclid.acta/1485889465

Digital Object Identifier
doi:10.1007/BF02392210

Zentralblatt MATH identifier
0142.38102

Rights
1966 © Almqvist & Wiksells Boktryckeri AB

Citation

Hartman, Philip; Stampacchia, Guido. On some non-linear elliptic differential-functional equations. Acta Math. 115 (1966), 271--310. doi:10.1007/BF02392210. http://projecteuclid.org/euclid.acta/1485889465.


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References

  • Bonnessen, T. & Fenchel, W., Theorie der konvexen Körper. Ergeb. Math. (Berlin) 1934.
  • Bers, L., John, F. & Schecter, M., Partial differential equations. (New York) 1964, Part II, Chapter 5.
  • Browder, F. E., Non-linear elliptic boundary value problems II. Trans. Amer. Math. Soc., 117 (1965), 530–550.
  • de Giorgi, E., Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari. Mem. Accad. Sci. Torino, 3 (1957), 25–43.
  • Gilbarg, D., Boundary value problems for nonlinear elliptic equations in n variables. Symposium on Nonlinear Problems, Madison (Wisconsin) 1962.
  • Hartman, P., On the bounded slope condition. To appear, Pacific J. Math.
  • 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 in Russian Math. Surveys, 16 (1961), 17–91.
  • 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.
  • Lewy, H., Über die Methode der Differenzengleichungen zur Lösung von Variations-und Randwertproblemen. Math. Ann., 98 (1928), 107–124.
  • Minty, G. J., Monotone (non-linear) operators in Hilbert space. Duke Math. J., 29 (1962), 341–346.
  • Miranda, M., Un teorema di esistenza e unicità per il problema dell'area minima in n variabili. Ann. Scuola Norm. Sup. Pisa, 19 (1965), 233–249.
  • Rado, T., On the problem of Plateau. Ergeb. Math. (Berlin) 1933.
  • Serrin, T., Local behavior of solutions of quasi-linear equations. Acta Math., 111 (1964), 247–302.
  • Stampacchia, G., On some regular multiple integral problems in the calculus of variations. Comm. Pure Appl. Math., 16 (1963), 383–421.
  • Stampacchia, G., Formes bilinéaires coercitives sur les ensembles convexes. C. R. Acad. Sci. Paris, 258 (1964), 4413–4416.