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Minimal boundaries enclosing a given volume. (English) Zbl 0481.49035


MSC:

49Q05 Minimal surfaces and optimization
49J20 Existence theories for optimal control problems involving partial differential equations
35R35 Free boundary problems for PDEs
49Q20 Variational problems in a geometric measure-theoretic setting
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
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References:

[1] ANZELLOTTI, G., GIAQUINTA, M., MASSARI, U., MODICA, G., PEPE, L.: Note sul problema di Plateau. Pisa: Editrice Tecnico Scientifica 1974
[2] CHEN, J.T.: On the existence of capillary free surfaces in the absence of gravity. Doctoral dissertation. Stanford University (1979)
[3] CONCUS, P., FINN, R.: On capillary free surfaces in the absence of gravity. Acta Math.132, 177-198 (1974) · Zbl 0382.76003
[4] DE GIORGI, E., COLOMBINI, F., PICCININI, L.: Frontiere orientate di misura minima e questione collegate. Pisa: Editrice Tecnico Scientifica 1972 · Zbl 0296.49031
[5] FINN, R.: Existence and non existence of capillary surfaces. Manuscripta Math.28, 1-11 (1979) · Zbl 0421.49043
[6] FINN, R., GIUSTI, E.: Non existence and existence of capillary surfaces. Manuscripta Math.28, 13-20 (1979) · Zbl 0466.53027
[7] GERHARDT, C.: On the capillarity problem with constant volume. Ann. Scuola Norm. Sup. Pisa (4)2, 303-320 (1975) · Zbl 0321.76010
[8] GIAQUINTA, M.: Regolarità delle superfici BV(?) con curvatura media assegnata. Boll. U.M.I.8, 567-578 (1973) · Zbl 0274.35028
[9] GIAQUINTA, M.: On the Dirichlet problem for surfaces of prescribed mean curvature. Manuscripta Math.12, 73-86 (1974) · Zbl 0276.35038
[10] GIUSTI, E.: Generalized solutions for the mean curvature equation. To appear · Zbl 0461.49024
[11] GIUSTI, E.: The equilibrium configuration of liquid drops. To appear in J. für Reine und Angew. Math. · Zbl 0438.76078
[12] GONZALEZ, E., MASSARI, U., TAMANINI, I.: On the regularity of boundaries of sets minimizing perimeter with a volume constraint. To appear · Zbl 0486.49024
[13] MASSARI, U.: Esistenza e regolarità delle ipersuperfici di curvatura media assegnata in ?n. Arch. Rat. Mech. Anal.55, 357-382 (1974) · Zbl 0305.49047
[14] MASSARI, U., PEPE, L.: Successioni convergenti di ipersuperfici di curvatura media assegnata. Rend. Sem. Mat. Univ. Padova53, 53-68 (1975) · Zbl 0358.49020
[15] MIRANDA, M.: Existence and regularity of hypersurfaces of ?n with prescribed mean curvature. Proceedings of Symposia in Pure Mathematics,23 (1973) · Zbl 0274.35022
[16] MIRANDA, M.: Frontiere minimali con ostacoli. Ann. Univ. Ferrara16, 29-37 (1971) · Zbl 0266.49036
[17] SERRIN, J.: The problem of Dirichlet for quasilinear elliptic equations with many independent variables. Phil. Trans. Royal Soc. London264, 413-496 (1969) · Zbl 0181.38003
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