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


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
Full Text: DOI EuDML


[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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