Pacific Journal of Mathematics

Evolutionary existence proofs for the pendant drop and $n$-dimensional catenary problems.

Andrew Stone

Article information

Pacific J. Math., Volume 164, Number 1 (1994), 147-178.

First available in Project Euclid: 8 December 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations
Secondary: 58E50: Applications 76B45: Capillarity (surface tension) [See also 76D45]


Stone, Andrew. Evolutionary existence proofs for the pendant drop and $n$-dimensional catenary problems. Pacific J. Math. 164 (1994), no. 1, 147--178.

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  • [Br] K. A. Brakke, The motion of a surfaceby its mean curvature,Math. Notes, Princeton Univ. Press, Princeton, NJ, 1978.
  • [CF] P. Concus and R. Finn, On capillaryfree surfacesin a gravitationalfield,Acta Math., 132(1974), 207-223.
  • [DH] U. Dierkes and G. Huisken, The n-dimensionalanalogue of the catenary: existence and non-existence,Pacific J. Math., 141 (1990), 47-54.
  • [Ec] K. Ecker, Estimates for evolutionarysurfaces of prescribed meancurvature, Math. Z., 180 (1982), 179-192.
  • [EH] K. Ecker and G. Huisken, Mean curvatureevolution of entire graphs,Annals of Math., 130 (1989), 453-471.
  • [Fi] R. Finn,Equilibrium Capillary Surfaces, Springer-Verlag, New York, 1986.
  • [Gel] C. Gerhardt, Evolutionarysurfacesof prescribed mean curvature, J. Differen- tial Equations, 36 (1980), 139-172.
  • [Ge2] C. Gerhardt, Globalregularityof the solutionsto the capillarity problem, Ann. Scuola Norm. Sup. Pisa Ser. (4), 3 (1976), 157-175.
  • [Gi] E. Giusti, The pendant water drop.A direct approach,Boll. Un. Mat. ItaL, 17 (1980), 458-465.
  • [GT] D. Gilbarg and N. S. Trudinger, Elliptic Partial DifferentialEquations ofSec- ond Order,2nd ed., A series of comprehensive studies in mathematics, vol. 224, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1983.
  • [Hul] G. Huisken, Capillary surfacesin negativegravitational fields, Math. Z., 185 (1984), 449-464.
  • [Hu2] G. Huisken, Non-parametric mean curvatureevolution with boundary conditions,J. Differential Equations, 77 (1989), 369-378.
  • [Hu3] G. Huisken, Flow by mean curvature of convex surfaces into spheres,J. Differential Geom., 20 (1984), 237-266.
  • [KS] D. Kinderlehrer and G. Stampacchia,An Introduction to VaratonalInequal- ities and Their Applications, Academic Press, New York and London, 1980.
  • [LT] A. Lichnewski and R. Temam, Surfaces minimales d'evolution: Le concept de pseudosolution, C. R. Acad. Sci. Paris, 284 (1977), 853-856.