Le problème des surfaces à courbure moyenne prescrite

Bethuel, F.; Rey, O.

Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1992-1993), Exposé no. 5, 17 p.

MR 1240546

@article{SEDP_1992-1993____A5_0,
     author = {B\'ethuel, Fabrice and Rey, O.},
     title = {Le probl\`eme des surfaces \`a courbure moyenne prescrite},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
     note = {talk:5},
     publisher = {Ecole Polytechnique, Centre de Math\'ematiques},
     year = {1992-1993},
     mrnumber = {1240546},
     language = {fr},
     url = {www.numdam.org/item/SEDP_1992-1993____A5_0/}
}

Bethuel, F.; Rey, O. Le problème des surfaces à courbure moyenne prescrite. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1992-1993), Exposé no. 5, 17 p. http://www.numdam.org/item/SEDP_1992-1993____A5_0/

Bibliographie

[1] F. Bethuel, Weak convergence of Palais-Smale sequences for some critical functionals, to appear. | MR 1261547

[2] F. Bethuel, O. Rey, Multiple solutions to the Plateau problem for nonconstant mean curvature, to appear in Duke Math. J. | MR 1262929 | Zbl 0815.53010

[3] H. Brezis, J.M. Coron, Multiple solutions of H-Systems and Rellich's conjecture, Comm. Pure Applied Math. 37, (1984), pp. 149-187. | MR 733715 | Zbl 0537.49022

[4] H. Brézis, J.M. Coron, Convergence of solutions of H-Systems or how to blow bubbles, Arch. Rat. Mech. Anal. 89, (1985), pp. 21-56. | MR 784102 | Zbl 0584.49024

[5] M. Grüter, Regularity of weak H-Surfaces, J. Reine Angew. Math. 329, pp. 1-15. | MR 636440 | Zbl 0461.53029

[6] E. Heinz, Über die Existenz einer Fläche konstanter mittlerer Krümmung bei vorgegebener Berandung, Math. Ann. 127, (1954), pp. 258-287. | MR 70013 | Zbl 0055.15303

[7] S. Hildebrandt, Randwertprobleme für Flächen mit vorgeschriebener mittlerer Krümmumg und Anwendungen auf die Kapillaritätstheorie, Math. Z.112, (1969), pp. 205-213. | MR 250208 | Zbl 0175.40403

[8] D. Hoffmann, J. Spruck, Sobolev and isoperimetric inequalities for riemannian submanifolds, Comm. Pure Appl. Math. 27, (1974), pp. 715-727, et 28, (1975), pp. 765-766. | MR 365424 | Zbl 0295.53025

[9] C. Morrey, Multiple integrals in the calculus of variations, Springer, Berlin (1966). | MR 202511 | Zbl 0142.38701

[10] O. Rey, Heat flow for the equation of surfaces with prescribed mean curvature, Math. Ann. 291, (1991), pp. 123-146. | MR 1125012 | Zbl 0761.58052

[11] J. Sacks, K. Uhlenbeck, The existence of minimal immersions of spheres, Ann. Math. 113, (1981), pp. 1-24. | MR 604040 | Zbl 0462.58014

[12] J. Sacks, K. Uhlenbeck, Minimal immersions of closed Riemann surfaces, Trans. Amer. Math. Soc. 271, (1982), pp. 639-652. | MR 654854 | Zbl 0527.58008

[13] K. Steffen, On the existence of surfaces with prescribed mean curvature and boundary, Math. Z. 146, (1976), pp. 113-135. | MR 394394 | Zbl 0343.49016

[14] K. Steffen, On the uniqueness of surfaces with prescribed mean curvature spanning a given contour, Arch. Rat. Mech. Anal. 94, (1986), pp. 101-122. | MR 832287 | Zbl 0678.49036

[15] M. Struwe, Nonuniqueness in the Plateau problem for surfaces of constant mean curvature, Arch. Rat. Anal. 93, (1986), pp. 135-157. | MR 823116 | Zbl 0603.49027

[16] M. Struwe, Large H-surfaces via the mountain-pass Lemma, Math. Ann. 270, (1985), pp. 441-459. | MR 774369 | Zbl 0582.58010

[17] M. Struwe, Plateau's problem and the Calculus of Variations, Mathematical Notes 35, Princeton University Press (1988). | MR 992402 | Zbl 0694.49028

[18] M. Struwe, Multiple solutions to the Dirichlet problem for the equation of prescribed mean curvature, Analysis, et cetera, Academic Press, Boston (1990). | MR 1039366 | Zbl 0703.53049

[19] G. Wang, The Dirichlet problem for the equation of prescribed mean curvature, Ann. Inst. Henri Poincaré, Anal. non linéaire, 9, (1992), pp. 643-655. | Numdam | MR 1198307 | Zbl 0784.53001

[20] H. Wente, An existence theorem for surfaces of constant mean curvature, J. Math.Analysis Appl. 26, (1969), pp. 318-344. | MR 243467 | Zbl 0181.11501

[21] H. Wente, A general existence theorem for surfaces of constant mean curvature, Math. Z. 120, (1971), pp. 277-278. | MR 282300 | Zbl 0214.11101

[22] H. Wente, The differential Δx = 2H(xu Λ xv) with vanishing boundary values, Proc. A.M.S. 50, (1975), pp. 113-137. | Zbl 0313.35030

[23] H. Werner, Das problem von Douglas für Flächen konstanter mittlerer Krümmung, Math. Ann. 133, (1957), pp. 303-319. | MR 95335 | Zbl 0077.34901