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Minimal boundaries enclosing a given volume. (English) Zbl 0481.49035
MSC:
49Q05Minimal surfaces (calculus of variations)
49J20Optimal control problems with PDE (existence)
35R35Free boundary problems for PDE
49Q20Variational problems in a geometric measure-theoretic setting
53A10Minimal surfaces, surfaces with prescribed mean curvature
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 · doi:10.1007/BF02392113
[4]DE GIORGI, E., COLOMBINI, F., PICCININI, L.: Frontiere orientate di misura minima e questione collegate. Pisa: Editrice Tecnico Scientifica 1972
[5]FINN, R.: Existence and non existence of capillary surfaces. Manuscripta Math.28, 1-11 (1979) · Zbl 0421.49043 · doi:10.1007/BF01647961
[6]FINN, R., GIUSTI, E.: Non existence and existence of capillary surfaces. Manuscripta Math.28, 13-20 (1979) · Zbl 0466.53027 · doi:10.1007/BF01647962
[7]GERHARDT, C.: On the capillarity problem with constant volume. Ann. Scuola Norm. Sup. Pisa (4)2, 303-320 (1975)
[8]GIAQUINTA, M.: Regolarità delle superfici BV(?) con curvatura media assegnata. Boll. U.M.I.8, 567-578 (1973)
[9]GIAQUINTA, M.: On the Dirichlet problem for surfaces of prescribed mean curvature. Manuscripta Math.12, 73-86 (1974) · Zbl 0276.35038 · doi:10.1007/BF01166235
[10]GIUSTI, E.: Generalized solutions for the mean curvature equation. To appear
[11]GIUSTI, E.: The equilibrium configuration of liquid drops. To appear in J. für Reine und Angew. Math.
[12]GONZALEZ, E., MASSARI, U., TAMANINI, I.: On the regularity of boundaries of sets minimizing perimeter with a volume constraint. To appear
[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 · doi:10.1007/BF00250439
[14]MASSARI, U., PEPE, L.: Successioni convergenti di ipersuperfici di curvatura media assegnata. Rend. Sem. Mat. Univ. Padova53, 53-68 (1975)
[15]MIRANDA, M.: Existence and regularity of hypersurfaces of ?n with prescribed mean curvature. Proceedings of Symposia in Pure Mathematics,23 (1973)
[16]MIRANDA, M.: Frontiere minimali con ostacoli. Ann. Univ. Ferrara16, 29-37 (1971)
[17]SERRIN, J.: The problem of Dirichlet for quasilinear elliptic equations with many independent variables. Phil. Trans. Royal Soc. London264, 413-496 (1969)