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Giusti, Enrico

On the equation of surfaces of prescribed mean curvature. Existence and uniqueness without boundary conditions. (English) Zbl 0381.35035

Invent. Math. 46, 111-137 (1978).
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Cited in 82 Documents

MSC:

35J60 Nonlinear elliptic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
53A99 Classical differential geometry
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Full Text: DOI EuDML

References:

[1] Bernstein, S.N.: Sur les surfaces définies au moyen de leur courbure moyenne ou totale. Ann. Ec. Norm. Sup.27, 233-256 (1909)
[2] Bombieri, E., Giusti, E.: Unpublished
[3] DeGiorgi, E.: Su una teoria generale della misura (r?1)-dimensionale in uno spazio adr dimensioni. Ann. di Matem. Pura e Appl. IV,36, 191-213 (1954) · Zbl 0055.28504 · doi:10.1007/BF02412838
[4] Emmer, M.: Superfici di curvatura media assegnata con ostacolo. Ann. di Matem. Pura e Appl.109, 371-389 (1976) · Zbl 0336.53003 · doi:10.1007/BF02416969
[5] Federer, H.: Geometric measure theory. Berlin, Heidelberg, New York: Springer 1969 · Zbl 0176.00801
[6] Finn, R.: Remarks relevant to minimal surfaces, and to surfaces of prescribed mean curvature. Journ. d’Anal. Math.14, 139-160 (1965) · Zbl 0163.34604 · doi:10.1007/BF02806384
[7] Finn, R.: A note on the capillary problem. Acta Math.132, 199-205 (1974) · Zbl 0382.76004 · doi:10.1007/BF02392114
[8] Finn, R., Giusti, E.: On non-parametric surfaces of constant mean curvature. Ann. Scuola Norm. Sup. Pisa. (4),4, 13-31 (1977) · Zbl 0343.53004
[9] Giaquinta, M.: Regolarità delle superficiBV(?) con curvatura media assegnata. Boll. U.M.I.8, 567-578 (1973) · Zbl 0274.35028
[10] Giaquinta, M.: On the Dirichlet problem for surfaces of prescribed mean curvature. Manusc. Math.12, 73-86 (1974) · Zbl 0276.35038 · doi:10.1007/BF01166235
[11] Giusti, E.: Boundary value problems for non-parametric surfaces of prescribed mean curvature. Ann. Scuola Norm. Sup. Pisa. (4)3, 501-548 (1976) · Zbl 0344.35036
[12] Hopf, E.: Elementare Bemerkungen über die Lösungen partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus. Berlin, Sber. Pruss. Akad. Wiss.19, 147-152 (1927) · JFM 53.0454.02
[13] Massari, U., Pepe, L.: Sull’approssimazione degli aperti lipschitziani di ? n con varietà differenziabili. Boll. U.M.I. (4)10, 532-544 (1974) · Zbl 0316.49031
[14] Massari, U., Pepe, L.: Sulle successioni convergenti di superfici a curvatura media assegnata. Rend. Sem. Mat. Padova.53, 53-68 (1975) · Zbl 0358.49020
[15] Miranda, M.: Superfici cartesiane generalizzate ed insiemi di perimetro finito sui prodotti cartesiani. Ann. Scuola Norm. Sup. Pisa18, 515-542 (1964) · Zbl 0152.24402
[16] Miranda, M.: Comportamento delle successioni convergenti di frontiere minimali. Rend. Sem. Mat. Padova38, 238-257 (1967) · Zbl 0154.37102
[17] Miranda, M.: Superfici minime illimitate. Ann. Scuola Norm. Sup. Pisa. (4)4, 313-322 (1977) · Zbl 0352.49020
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