Principe du maximum local et solutions généralisées de problèmes du type hypersurfaces minimales
Bulletin de la Société Mathématique de France, Tome 102 (1974), p. 417-433
@article{BSMF_1974__102__417_0,
     author = {Lichnewsky, Alain},
     title = {Principe du maximum local et solutions g\'en\'eralis\'ees de probl\`emes du type hypersurfaces minimales},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {102},
     year = {1974},
     pages = {417-433},
     doi = {10.24033/bsmf.1787},
     zbl = {0301.49029},
     mrnumber = {51 \#1566},
     language = {fr},
     url = {http://http://www.numdam.org/item/BSMF_1974__102__417_0}
}
Lichnewsky, Alain. Principe du maximum local et solutions généralisées de problèmes du type hypersurfaces minimales. Bulletin de la Société Mathématique de France, Tome 102 (1974) pp. 417-433. doi : 10.24033/bsmf.1787. http://www.numdam.org/item/BSMF_1974__102__417_0/

[1] Bombieri (E.), De Giorgi (E.) et Miranda (M.). - Una maggiorazione a priori relativa alle ipersuperfici minimali non parametriche, Arch. rat. Mech. and Anal., t. 32, 1969, p. 255-267. | MR 40 #1898 | Zbl 0184.32803

[2] Bronsted (A.) et Rockafellar (R. T.). - On the subdifferentiability of convex functions, Proc. Amer. Math. Sc., t. 16, 1965, p. 605-611. | MR 31 #2361 | Zbl 0141.11801

[3] Ekeland (I.) et Temam (R.). - Analyse convexe et problèmes variationnels. - Paris, Dunod-Bordas, 1974. | MR 57 #3931a | Zbl 0281.49001

[4] Gagliardo (E.). - Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in n-variabili, Rend. Sem. Mat. Padova, t. 27, 1957, p. 284-305. | Numdam | MR 21 #1525 | Zbl 0087.10902

[5] Krasnolselsk'Ij (M. A.). - Topological methods in the theory of non-linear integral equations. - Oxford, Pergamon Press, 1964 (International Series of Monographs on pure and applied Mathematics, 45). | Zbl 0111.30303

[6] Ladyženskaja (O. A.) et Ural'Ceva (N. N.). - Linear and quasilinear elliptic equations. - New York, Academic Press, 1968 (Mathematics in Science and Engineering, 46). | Zbl 0164.13002

[7] Ladyženskaja (O. A.) et Ural'Ceva (N. N.). - Local estimates for gradients of solutions of non-uniformly elliptic and parabolic equations, Comm. pure and appl. Math., t. 23, 1970, p. 677-703. | MR 42 #654 | Zbl 0193.07202

[8] Lichnewsky (A.). - Principe du maximum local et solutions généralisées de problèmes du type hypersurface minima, Thèse 3e cycle, Univ. Paris-Sud Orsay, 1973.

[9] Lions (J. L.). - Problèmes aux limites dans les équations aux dérivées partielles. - Montréal, Presses de l'Université de Montréal, 1962 (Séminaire de Mathématiques supérieures. Été 1962, 1). | Zbl 0143.14003

[10] Miranda (M.). - Existence and regularity of hypersurfaces of Rn with prescribed mean curvature, "Partial differential equations. Proceedings of the symposium held at Berkeley, 1971", p. 1-9. - Providence, American mathematical Society, 1973 (Proceedings of Symposia in pure Mathematics, 23). | Zbl 0274.35022

[11] Miranda (M.). - Un teorema di esistenza e unicita per il problema dell'area minima in n variabili, Ann. Scuola, norm. sup. Pisa, t. 19, 1965, p. 233-249. | Numdam | MR 31 #6144 | Zbl 0137.08201

[12] Moreau (J. J.). - Weak and strong solutions of dual problems, "Contributions to non-linear functional analysis. Proceedings of a symposium, held at Madison, 1971". - New-York, Academic Press, 1971. | Zbl 0274.49007

[13] Rockafellar (R. T.). - Integrals which are convex functionnals, Pacific J. of Math., t. 24, 1968, p. 525-529; et t. 39 p. 439-469, 1971. | Zbl 0159.43804

[14] Rockafellar (R. T.). - Convex analysis. - Princeton, Princeton University Press, 1970 (Princeton mathematical Series, 28). | MR 43 #445 | Zbl 0193.18401

[15] Schwartz (L.). - Théorie des distributions. Nouvelle édition. - Paris, Hermann, 1966 (Publ. Inst. Math. Univ. Strasbourg, 9-10). | MR 35 #730 | Zbl 0149.09501

[16] Serrin (J.). - The Problem of Dirichlet for quasilinear elliptic differential equations with many independent variables, Phil. Trans. Royal Soc. Lond., t. A. 264, 1969, p. 413-496. | MR 43 #7772 | Zbl 0181.38003

[17] Serrin (J.). - Local behaviour of quasilinear equations, Acta Math., Uppsala, t. 111, 1964, p. 247-302. | MR 30 #337 | Zbl 0128.09101

[18] Stampacchia (G.). - Équations elliptiques du second ordre à coefficients discontinus. - Montréal, Presses de l'Université de Montréal, 1966, Séminaire de mathématiques supérieures. Été 1965, 16). | Zbl 0151.15501

[19] Stampacchia (G.). - On some regular multiple integral problems in the calculus of variations, Comm. pure and appl. Math., t. 16, 1963, p. 383-421. | MR 27 #5148 | Zbl 0138.36903

[20] Temam (R.). - Calcul des variations, Cours de 3e cycle, Université d'Orsay, 1970/1971 (Publications mathématiques d'Orsay).

[21] Temam (R.). - Solutions généralisées de certaines équations du type hypersurfaces minimales, Arch. rat. Mech. and Anal., t. 44, 1971, p. 121-156. | MR 49 #3647 | Zbl 0252.49002

[22] Trudinger (N. S.). - On the analicity of generalized minimal surfaces, Bull. Austral. math. Soc., t. 5, 1971, p. 315-320. | MR 46 #501 | Zbl 0231.35014