Regularity properties of H-graphs

Commentarii Mathematici Helvetici

Volumn 73, Issue 3, 1998, Pages 379-399

  Finn, Robert ^a   Lu, Jianan ^b  

^a STANFORD UNIVERSITY   (United States)

^b IBM   (United States)

Author keywords

Capillarity; H graph, gradient estimate; Harnack inequality; Mean curvature; Moon surface

Indexed keywords

EID: 0032432049     PISSN: 00102571     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000140050060     Document Type: Article

References (30)

1. S.N. Bernstein, Sur les surfaces définie au moyen de leur courbure moyenne et totale, Ann. Sci. École Norm. Sup. 27 (1910), 233-256.
2. E. Bombieri and E. Giusti, Local estimates for the gradient of non-parametric surfaces of prescribed mean curvature, Comm. Pure Applied Math. 26 (1973), 381-394.
3. K.-S. Chua, Absolute gradient bound for surfaces of constant mean curvature, Annali Sc. Norm. Sup. 21 (1994), 1-9.
4. P. Concus and R. Finn, On capillary free surfaces in the absence of gravity, Acta Math. 132 (1974), 177-198.
5. L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, Boca Raton 1992.
6. R. Finn, Gradient and Gauss-curvature bounds for H-graphs, pp. 137-150. In: Xin Zhi Liu and David Siegel (Eds.), Comparison Methods and Stability Theory, Marcel Dekker 1994.
7. R. Finn, On equations of minimal surface type, Annals of Math. 60 (1954), 397-416.
8. R. Finn, New estimates for equations of minimal surface type, Arch Rat. Mech. Anal. 14 (1963), 337-375.
9. R. Finn, Remarks relevant to minimal surfaces and to surfaces of prescribed mean curvature, J. Analyse Math. 14 (1965), 139-160.
10. R. Finn, Partial differential equations whose solutions admit no isolated singularities, Scripta Math. 26 (1961), 107-115.
11. R. Finn, Moon surfaces, and boundary behaviour of capillary surfaces for perfect wetting and nonwetting, Proc. London Math. Soc. 57 (1988), 542-576.
12. R. Finn, The inclination of an H-graph, Springer-Verlag Lecture Notes 1340 (1988), 40-60.
13. R. Finn, Equilibrium Capillary Surfaces, Springer-Verlag, New York 1986.
14. R. Finn, A note on the capillary problem, Acta Math. 132 (1974), 199-206.
15. R. Finn and E. Giusti, On nonparametric surfaces of constant mean curvature, Ann. Scuola Normale Sup. Pisa 4 (1977), 13-31.
16. E. Giusti, On the equation of surfaces of prescribed mean curvature: existence and uniqueness without boundary conditions, Invent. Math. 46 (1978), 111-137.
17. E. Giusti, Minimal Surfaces and Functions of Bounded Variation, Birkhäuser Verlag, Boston 1984.
18. E. Heinz, Über Flächen mit eindeutiger Projektion auf einer Ebene, deren Krümmungen durch Ungleichungen eingeschränkt sind, Math. Ann. 129 (1955), 451-454.
19. P. Hartman, On elliptic partial differential equations and uniqueness theorems for closed surfaces, J. Math. Mech. 7 (1958), 377-392.
20. D. Hilbert, Über das Dirichlet'sche Princip, Jahresber. deutschen Math.-Ver. 8 (1900), 184-188.
21. H. Jenkins and J. Serrin, Variational problems of minimal surface type I, Arch. Rat. Mech. Anal. 12 (1963), 185-212.
22. N.J. Korevaar, An easy proof of the prescribed gradient bound for solutions to the prescribed mean curvature equation, Proc. Symp. Pure Math. 45 (1986), Part 2, 81-89.
23. G.M. Lieberman, Gradient estimates for capillary type problems via the maximum principle, Comm. in P.D.E. 13 (1988), 33-59.
24. F.-T. Liang, An absolute gradient bound for nonparametric surfaces of prescribed mean curvature, Ind. Univ. Math. J. 41 (1992), 569-604.
25. n, Arch. Rat. Mech. Anal. 55 (1974), 257-282.
26. M. Miranda, Superfici cartesiane generalizzate ed insiemi di perimetro finito sui prodotti cartesiani, Ann. Scuola Norm. Sup. Pisa 18 (1964), 515-542.
27. M. Miranda, Superfici minime illimitate, Ann. Scuola Norm. Sup. Pisa 4 (1977), 313-322.
28. F. Sauvigny, A new proof of the gradient estimate for graphs of prescribed mean curvature, Manuscr. Math. 74 (1992), 83-86.
29. J.B. Serrin, The Dirichlet problem for surfaces of constant mean curvature, Proc. Lon. Math. Soc. 21 (1970), 361-384.
30. L. Simon, Equations of mean curvature type in two independent variables, Pac. J. Math. 69 (1977), 245-268.