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The Dirichlet problem with a volume constraint. (English) Zbl 0268.35031


MSC:

35J20 Variational methods for second-order elliptic equations
35J25 Boundary value problems for second-order elliptic equations
35J65 Nonlinear boundary value problems for linear elliptic equations
35J45 Systems of elliptic equations, general (MSC2000)
49R50 Variational methods for eigenvalues of operators (MSC2000)
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References:

[1] CESARI, L.: Surface Area, Ann. of Math. Studies No. 35, Princeton, (1956). · Zbl 0073.04101
[2] HEINZ, E.: On surfaces of constant mean curvature with polygonal boundaries, Arch. Rat. Mech. Analysis 36, No. 5 335-347, (1970). · Zbl 0191.12002 · doi:10.1007/BF00282270
[3] HEINZ, E.: Unstable surfaces of constant mean curvature, Arch. Rat. Mech. Analysis 38, No. 4, 257-267, (1970) · Zbl 0203.53804 · doi:10.1007/BF00281523
[4] MORREY, C.B.: On the solutions of quasi-linear elliptic partial differential equations, Trans. Amer. Math. Soc. 43, 126-166, (1938). · Zbl 0018.40501 · doi:10.1090/S0002-9947-1938-1501936-8
[5] STEFFEN, K.: Ein verbessenen Existenzsatz für Flächen konstanter mittlerer Krümmung, Manuscripta Math. 6, 105-139, (1972). · Zbl 0229.53011 · doi:10.1007/BF01369709
[6] STEFFEN, K.: Flächen konstanter mittlerer Krümmung mit vorgegebenem Volumen oder Flächeninhalt, Arch. Rat. Mech. Analysis 49, No. 2, 99-128, (1972). · Zbl 0259.53043 · doi:10.1007/BF00281413
[7] WENTE, H.: An existence theorem for surfaces of constant mean curvature, J. Math. Analysis Appl. 26, 318-344, (1969) · Zbl 0181.11501 · doi:10.1016/0022-247X(69)90156-5
[8] WENTE, H.: A general existence theorem for surfaces of constant mean curvature, Math. Z. 277-288, (1971). · Zbl 0214.11101
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