On the capillarity problem with constant volume
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 2 (1975) no. 2, p. 303-320 
@article{ASNSP_1975_4_2_2_303_0,
     author = {Gerhardt, Claus},
     title = {On the capillarity problem with constant volume},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 2},
     number = {2},
     year = {1975},
     pages = {303-320},
     zbl = {0321.76010},
     mrnumber = {390897},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1975_4_2_2_303_0}
}

Gerhardt, Claus. On the capillarity problem with constant volume. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 2 (1975) no. 2, pp. 303-320. http://www.numdam.org/item/ASNSP_1975_4_2_2_303_0/

[1] P. Concus - R. Finn, On a class of capillary surfaces, J. Analyse Math., 23 (1970), pp. 65-70. | MR 273889 | Zbl 0257.76007

[2] P. Concus - R. Finn, On capillary free surfaces in a gravitational field, Acta Math., 132 (1974), pp. 207-223. | MR 670443 | Zbl 0382.76005

[3] P. Concus - R. Finn, On capillary free surfaces in the absence of gravity, Acta Math., 132 (1974), pp. 177-198. | MR 670441 | Zbl 0382.76003

[4] M. Emmer, Esistenza, unicità e regolarità delle superfici di equilibrio nei capillari, Ann. Univ. Ferrara, n. 0, Ser., Sez. VII, 18 (1973), pp. 79-94. | MR 336507 | Zbl 0275.49005

[5] R. Finn, A note on the capillary problem, Acta Math., 132 (1974), pp. 199-205. | MR 670442 | Zbl 0382.76004

[6] R. Finn, Capillarity phenomena, to appear in Uspehi Mat. Nauk. | MR 484001 | Zbl 0325.76046

[7] C. Gerhardt, Existence and regularity of capillary surfaces, Boll. Un. Mat. Ital., Ser. IV, 10 (1974), pp. 317-335. | MR 365316 | Zbl 0314.49019

[8] C. Gerhardt, Existence, regularity, and boundary behaviour of generalized surfaces of prescribed mean curvature, Math. Z., 139 (1974), pp. 173-198. | MR 437925 | Zbl 0316.49005

[9] S. Hildebrandt - H.C. Wente, Variational problems with obstacles and a volume constraint, Math. Z., 135 (1973), pp. 55-68. | MR 365314 | Zbl 0284.49017

[10] H. Minkowski, Kapillarität, Encyclopädie der Mathematischen Wissenschaften, Vol. VI, pp. 559-613, Leipzig: Teubner 1903-1921.

[11] J Nečas, Les méthodes directes en théorie des équations elliptiques, Masson et Cie, Paris, 1967. | MR 227584

[12] L. Schwartz, Théorie des distributions, Hermann, Paris, 1966. | MR 209834 | Zbl 0149.09501

[13] G. Stampacchia, Equations elliptiques du second ordre à coefficient discontinus, Sem. Math. Sup., Université de Montréal, 1966. | MR 251373 | Zbl 0151.15501

[14] K. Steffen, Flächen konstanter mittlerer Krümmung mit vorgegebenem Volumen oder Flächeninhalt, Arch. Rat. Mech. Analysis, 49 (1972), pp. 99-128. | MR 341261 | Zbl 0259.53043

[15] H.C. Wente, A general existence theorem for surfaces of constant mean curvature, Math. Z., 120 (1971), pp. 277-288. | MR 282300 | Zbl 0214.11101

[16] H.C. Wente, An existence theorem for surfaces in equilibrium satisfying a volume constraint, Arch. Rat. Mech. Analysis, 50 (1973), pp. 139-158. | MR 336563 | Zbl 0268.49051