Interior curvature estimates for hypersurfaces of prescribed mean curvature

 Access to full text

 Full (PDF)

1. [1] E. Bombieri, E. De Giorgi and M. Miranda, Una maggiorazione apriori relative alle ipersuperfici minimali non parametriche, Arch. Rat. Mech. Anal., Vol. 32, 1969, pp. 255-269. Zbl0184.32803
2. [2] L. Caffarelli, L. Nirenberg and J. Spruck, On a Form of Bernstein's Theorem, preprint (to appear). Zbl0668.35028MR864651
3. [3] P. Concus and R. Finn, On Capillary Free Surfaces in a Gravitational Field, Acta Math., Vol. 132, 1974, pp. 207-223. Zbl0382.76005MR670443
4. [4] K. Ecker, An Interior Gradient Bound for Solutions of Equations of Capillary Type, Arch. Rat. Mech. Anal., Vol. 92, 1986, pp. 137-151. MR816617
5. [5] K. Ecker and G. Huisken, A Bernstein Result for Minimal Graphs of Controlled Growth, J. Diff. Geom. (to appear). Zbl0696.53002MR1037408
6. [6] R. Finn, On Equations of Minimal Surface Type, Ann. of Math. (2), Vol. 60, 1954, pp. 397-415. Zbl0058.32501MR66533
7. [7] D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order (2nd edition), Springer-Verlag, Berlin-Heidelberg, New York, 1983. Zbl0562.35001MR737190
8. [8] E. Heinz, Über die Lösungen der Minimalflächengleichung, Nachr. Akad. Wiss. Göttingen Math. Phys. Kl, Vol. II, 1952, pp. 51-56. Zbl0048.15401MR54182
9. [9] E. Heinz, Interior Gradient Estimates for Surfaces z = F (x, y) with Prescribed Mean Curvature, J. Diff. Geom., Vol. 5, 1971, pp. 149-157. Zbl0212.44001MR289940
10. [10] N. Korevaar, An Easy Proof of the Interior Gradient Bound for Solutions to the Prescribed Mean Curvature Equation, Proc. Symp. Pure Math., Vol. 45, 1986, Part 2. Zbl0599.35046MR843597
11. [11] O.A. Ladyzhenskaya and N.N. Ural'tseva, Local Estimates for Gradients of Solutions of Nonuniformly Elliptic and Parabolic Equations, Comm. Pure Appl. Math., Vol. 23, 1970, pp. 677-703. Zbl0193.07202MR265745
12. [12] J. Michael and L. Simon, Sobolev and Mean Value Inequalities on Generalized Submanifolds of R", Comm. Pure Appl. Math., Vol. 26, 1973, pp. 361-379. Zbl0256.53006MR344978
13. [13] J. Moser, A New Proof of De Giorgi's Theorem Concerning the Regularity Problem for Elliptic Differential Equations, Comm. Pure Appl. Math., Vol. 13, 1960, pp. 457- 468. Zbl0111.09301MR170091
14. [14] R. Schoen, L. Simon and S.T. Yau, Curvature Estimates for Minimal Hypersurfaces, Acta Math., Vol. 134, 1975, pp. 275-288. Zbl0323.53039MR423263
15. [15] L. Simon and J. Spruck, Existence and Regularity of a Capillary Surface with Prescribed Contact Angle, Arch. Rat. Mech. Anal., Vol. 61, 1976, pp. 19-34. Zbl0361.35014MR487724
16. [16] N.S. Trudinger, A New Proof of the Interior Gradient Bound for the Minimal Surface Equation in n-Dimensions, Proc. Nat. Acad. Sci. U.S.A., Vol. B69B, 1972. pp. 821-823. Zbl0231.53007MR296832
17. [17] N.S. Trudinger, Gradient Estimates and Mean Curvature, Math. Z., Vol. 131, 1973. pp. 165-175. Zbl0253.53003MR324187
18. [18] J.C.C. Nitsche, Lectures on Minimal Surfaces, Vol. I (to appear). Zbl0202.20601MR305255