The Dirichlet problem for the equation of prescribed mean curvature

Guofang Wang

Annales de l'I.H.P. Analyse non linéaire (1992)

  • Volume: 9, Issue: 6, page 643-655
  • ISSN: 0294-1449

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Wang, Guofang. "The Dirichlet problem for the equation of prescribed mean curvature." Annales de l'I.H.P. Analyse non linéaire 9.6 (1992): 643-655. <http://eudml.org/doc/78293>.

@article{Wang1992,
author = {Wang, Guofang},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {mountain pass theorem; Euler Lagrange equation; energy functional},
language = {eng},
number = {6},
pages = {643-655},
publisher = {Gauthier-Villars},
title = {The Dirichlet problem for the equation of prescribed mean curvature},
url = {http://eudml.org/doc/78293},
volume = {9},
year = {1992},
}

TY - JOUR
AU - Wang, Guofang
TI - The Dirichlet problem for the equation of prescribed mean curvature
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1992
PB - Gauthier-Villars
VL - 9
IS - 6
SP - 643
EP - 655
LA - eng
KW - mountain pass theorem; Euler Lagrange equation; energy functional
UR - http://eudml.org/doc/78293
ER -

References

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  2. [BC2] H. Brezis and J.-M. Coron, Convergence of Solutions of H-Systems or How to Blow Bubbles, Arch. Rational Mech. Anal., Vol. 89, 1985, pp. 21-56. Zbl0584.49024MR784102
  3. [He] E. Heinz, Uber die Regularität schwacher Lösungen nicht linearer elliptischer Systeme, Nachr. Akad. Wiss. Göttingen, Vol. II, No. 1, 1986. Zbl0627.35033MR846127
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  5. [Hi2] S. Hildebrandt, Randwertprobleme für Flächen mit vorgeschriebener mittlerer Krümmung und Anwendungen auf die Kapillaritätstheorie, Teil I. Fest vorgegebener, Rand. Math. Z., Vol. 112, 1969, pp.205-213. Zbl0175.40403MR250208
  6. [Pc] F. Pacard, Convergence of Surfaces of Prescribed Mean Curvature, Nonlinear Analysis. Theory, Methods & Applications, Vol. 13, 1989, pp. 1269-1281. Zbl0696.49070
  7. [Stf1] K. Steffen, On the Existence of Surfaces with Prescribed Mean Curvature and Boundary, Math. Z., Vol. 146, 1976, pp. 113-135. Zbl0343.49016MR394394
  8. [Stf2] K. Steffen, On the Non-Uniqueness of Surfaces with Prescribed Constant Mean Curvature Spanning a Given Contour, Arch. Rat. Mech. Anal., Vol. 94, 1986, pp. 101-122. Zbl0678.49036MR832287
  9. [Str1] M. Struwe, Plateau's Problem and the Calculus of Variations, Lecture Notes, Princeton University Press (in press). 
  10. [Str2] M. Struwe, Non-Uniqueness in the Plateau Problem for Surfaces of Constant Mean Curvature, Arch. Rat. Mech. Anal., Vol. 93, 1986, pp. 135-157. Zbl0603.49027MR823116
  11. [Str3] M. Struwe, Large H-Surfaces via the Mountain-Pass-Lemma, Math. Ann., Vol. 270, 1985, pp. 441-459. Zbl0582.58010MR774369
  12. [Str4] M. Struwe, Multiple Solutions to the Dirichlet Problem for the Equation of Prescribed Mean Curvature, preprint. MR1039366
  13. [Wet1] H.C. Wente, An Existence Theorem for Surfaces of Constant Mean Curvature, J. Math. Anal. Appl., Vol. 26, 1969, pp.318-344. Zbl0181.11501MR243467
  14. [Wet2] H.C. Wente, A General Existence Theorem for Surfaces of Constant Mean Curvature, Math. Z., Vol. 120, 1971, pp. 277-288. Zbl0214.11101MR282300
  15. [Wet3] H.C. Wente, The Differential Equation Δx = 2 H xu ∧ xv with Vanishing Boundary Values, Proc. A.M.S., Vol. 50, 1975, pp. 59-77. Zbl0313.35030MR374673

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