Duke Mathematical Journal

Existence and regularity for higher-dimensional H-systems

Frank Duzaar and Joseph F. Grotowski

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Duke Math. J. Volume 101, Number 3 (2000), 459-485.

Dates
First available in Project Euclid: 17 August 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1092749201

Mathematical Reviews number (MathSciNet)
MR1740684

Digital Object Identifier
doi:10.1215/S0012-7094-00-10133-0

Zentralblatt MATH identifier
0959.35050

Subjects
Primary: 58E15: Application to extremal problems in several variables; Yang-Mills functionals [See also 81T13], etc.
Secondary: 35B65: Smoothness and regularity of solutions 35J50: Variational methods for elliptic systems 35J60: Nonlinear elliptic equations 35J70: Degenerate elliptic equations

Citation

Duzaar, Frank; Grotowski, Joseph F. Existence and regularity for higher-dimensional H -systems. Duke Math. J. 101 (2000), no. 3, 459--485. doi:10.1215/S0012-7094-00-10133-0. http://projecteuclid.org/euclid.dmj/1092749201.


Export citation

References

  • R. Courant, Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces, Interscience, New York, 1950.
  • U. Dierkes, S. Hildebrandt, A. Küster, and O. Wohlrab, Minimal Surfaces, Vol. 1: Boundary Value Problems, Grundlehren Math. Wiss. 295; Vol. 2: Boundary Regularity, Grundlehren Math. Wiss. 296, Springer-Verlag, Berlin, 1992.
  • W. Ding and G. Tian, Energy identity for a class of approximate harmonic maps from surfaces, Comm. Anal. Geom. 3 (1995), 543--554.
  • F. Duzaar, Variational inequalities and harmonic mappings, J. Reine Angew. Math. 374 (1987), 39--60.
  • --. --. --. --., On the existence of surfaces with prescribed mean curvature and boundary in higher dimensions, Ann. Inst. H. Poincaré Anal. Non Linéaire 10 (1993), 191--214.
  • F. Duzaar and M. Fuchs, Existenz und Regularität von Hyperflächen mit vorgeschriebener mittlerer Krümmung, Analysis 10 (1990), 193--230.
  • --. --. --. --., On the existence of integral currents with prescribed mean curvature vector, Manuscripta Math. 67 (1990), 41--67.
  • --. --. --. --., Einige Bemerkungen über die Existenz orientierter Mannigfaltigkeiten mit vorgeschriebener mittlerer Krümmungsform, Z. Anal. Anwendungen 10 (1991), 525--534.
  • --. --. --. --., Einige Bemerkungen über die Regularität von stationären Punkten gewisser geometrischer Variationsintegrale, Math. Nachr. 152 (1991), 39--47.
  • --. --. --. --., A general existence theorem for integral currents with prescribed mean curvature form, Boll. Un. Mat. Ital. B (7) 6 (1992), 901--912.
  • F. Duzaar and K. Steffen, Boundary regularity for minimizing currents with prescribed mean curvature, Calc. Var. Partial Differential Equations 1 (1993), 355--406.
  • --. --. --. --., $\lambda$ minimizing currents, Manuscripta Math. 80 (1993), 403--447.
  • --. --. --. --., Existence of hypersurfaces with prescribed mean curvature in Riemannian manifolds, Indiana Univ. Math. J. 45 (1996), 1045--1093.
  • --. --. --. --., Parametric surfaces of least $H$-energy in a Riemannian manifold, Math. Ann. 314 (1999), 197--244.
  • L. C. Evans and R. F. Gariepy, Measure Theory and Fine Properties of Functions, Stud. Adv. Math., CRC Press, Boca Raton, Fla., 1992.
  • H. Federer, Geometric Measure Theory, Grundlehren Math. Wiss. 153, Springer-Verlag, Berlin, 1969.
  • R. Gulliver and J. Spruck, The Plateau problem for surfaces of prescribed mean curvature in a cylinder, Invent. Math. 13 (1971), 169--178.
  • --. --. --. --., Existence theorems for parametric surfaces of prescribed mean curvature, Indiana Univ. Math. J. 22 (1972), 445--472.
  • R. Hardt and F. Lin, Mappings minimizing the $L^p$ norm of the gradient, Comm. Pure Appl. Math. 40 (1987), 555--588.
  • E. Heinz, Über die Existenz einer Fläche konstanter mittlerer Krümmung bei vorgegebener Berandung, Math. Ann. 127 (1954), 258--287.
  • S. Hildebrandt, Einige Bemerkungen über Flächen beschränkter mittlerer Krümmung, Math. Z. 115 (1970), 169--178.
  • --. --. --. --., On the Plateau problem for surfaces of constant mean curvature, Comm. Pure Appl. Math. 23 (1970), 97--114.
  • S. Hildebrandt and H. Kaul, Two-dimensional variational problems with obstructions, and Plateau's problem for $H$-surfaces in a Riemannian manifold, Comm. Pure Appl. Math. 25 (1972), 187--223.
  • C. B. Morrey, Multiple Integrals in the Calculus of Variations, Grundlehren Math. Wiss. 130, Springer-Verlag, New York, 1966.
  • L. Mou and P. Yang, Multiple solutions and regularity of $H$-systems, Indiana Univ. Math. J. 45 (1996), 1193--1222.
  • J. Qing, On singularities of the heat flow for harmonic maps from surfaces into spheres, Comm. Anal. Geom. 3 (1995), 297--315.
  • J. Sacks and K. Uhlenbeck, The existence of minimal immersions of $2$-spheres, Ann. of Math. (2) 113 (1981), 1--24.
  • L. Simon, Lectures on Geometric Measure Theory, Proc. Centre Math. Appl. Austral. Nat. Univ. 3, Austral. Nat. Univ. Press, Canberra, 1983.
  • K. Steffen, Isoperimetric inequalities and the problem of Plateau, Math. Ann. 222 (1976), 97--144.
  • --. --. --. --., On the existence of surfaces with prescribed mean curvature and boundary, Math. Z. 146 (1976), 113--135.
  • H. Wente, An existence theorem for surfaces of constant mean curvature, J. Math. Anal. Appl. 26 (1969), 318--344.
  • H. Werner, Das problem von Douglas für Fläschen konstanter mittlerer Krümmung, Math. Ann. 133 (1957), 303--319.