Harnack's inequalities for solutions to the mean curvature equation and to the capillarity problem
Rendiconti del Seminario Matematico della Università di Padova, Tome 110 (2003), pp. 57-96. 
@article{RSMUP_2003__110__57_0,
     author = {Liang, Fei-Tsen},
     title = {Harnack's inequalities for solutions to the mean curvature equation and to the capillarity problem},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {57--96},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {110},
     year = {2003},
     mrnumber = {2033001},
     zbl = {1121.35056},
     language = {en},
     url = {http://archive.numdam.org/item/RSMUP_2003__110__57_0/}
}
TY  - JOUR
AU  - Liang, Fei-Tsen
TI  - Harnack's inequalities for solutions to the mean curvature equation and to the capillarity problem
JO  - Rendiconti del Seminario Matematico della Università di Padova
PY  - 2003
SP  - 57
EP  - 96
VL  - 110
PB  - Seminario Matematico of the University of Padua
UR  - http://archive.numdam.org/item/RSMUP_2003__110__57_0/
LA  - en
ID  - RSMUP_2003__110__57_0
ER  - 
%0 Journal Article
%A Liang, Fei-Tsen
%T Harnack's inequalities for solutions to the mean curvature equation and to the capillarity problem
%J Rendiconti del Seminario Matematico della Università di Padova
%D 2003
%P 57-96
%V 110
%I Seminario Matematico of the University of Padua
%U http://archive.numdam.org/item/RSMUP_2003__110__57_0/
%G en
%F RSMUP_2003__110__57_0
Liang, Fei-Tsen. Harnack's inequalities for solutions to the mean curvature equation and to the capillarity problem. Rendiconti del Seminario Matematico della Università di Padova, Tome 110 (2003), pp. 57-96. http://archive.numdam.org/item/RSMUP_2003__110__57_0/

[1] E. Bombieri - E. De Giorgi - E. Giusti, Una maggiorazione a priori relativa alle ipersuperifici minimali non parametriche, Arch. Rat. Mech. Anal., 32 (1969), pp. 255-267. | MR | Zbl

[2] M. Emmer, Esistenza, unicità e regolarità nelle superfici di equilibrio nei capillari, Ann. Univ. Ferrera Sez. VII, 18 (1973), pp. 79-94. | MR | Zbl

[3] R. Finn, Equilibrium Capillary Surfaces, Grundlehren der Mathem. Wiss. 284, Springer-Verlag, New York, 1986. | MR | Zbl

[4] R. Finn, The inclination of an H-graph, Springer-Verlag Lecture Notes, 1340 (1973), pp. 381-394. | MR | Zbl

[5] R. Finn - E. Giusti, On non-parametric syrfaces of constant mean curvature, Ann. Sc. Norm. Sup. Pisa, 4 (1977), pp. 13-31. | Numdam | MR | Zbl

[6] R. Finn - Jianan Lu, Some remarkable properties of H graphs, Mem. Diff. Equations Math. Physics, 12 (1997), pp. 57-61. | MR | Zbl

[7] C. Gerhardt, Existence, regularity, and boundary behavior of generalized surfaces of prescribed curvature, Math. Z., 139 (1974), pp. 173-198. | MR | Zbl

[8] C. Gerhardt, Global regularity of the solutions to the capillarity problems, Sup. Pisa, Sci. Fis. Mat. IV, Ser., 3 (1976), pp. 157-175. | Numdam | MR | Zbl

[9] C. Gerhardt, On the regularity of solutions to Variational Problems in BV(V), Math. Z., 149 (1976), pp. 281-286. | MR | Zbl

[10] D. Gilbarg - N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd Ed., Springer-Verlag, New York, 1983. | MR | Zbl

[11] E. Giusti, On the equation of surfaces of prescribed mean curvature: existence and uniqueness without boundary conditions, Invent. Math., 46 (1978), pp. 111-137. | EuDML | MR | Zbl

[12] E. Giusti, Generalized solutions for the mean curvature equation, Pacific J. Math., 88 (1980), pp. 297-321. | MR | Zbl

[13] E. Heinz, Interior gradient estimates for surfaces z4f(x, y) of prescribed mean curvature, J. Diff. Geom. (1971), pp. 149-157. | MR | Zbl

[14] O. A. Landyhenskaya - N. N. Uraltseva, Local estimates for gradients of solutions of non-uniformly elliptic and parabolic equations, Comm. Pure Appl. Math., 23 (1970), pp. 677-703. | MR | Zbl

[15] F. Liang, An absolute gradient bound for nonparametric surfaces of constant mean curvature, Indiana Univ. Math. J., 41(3) (1992), pp. 590-604. | MR | Zbl

[16] F. Liang, Absolute gradient bounds for nonparametric hypersurfaces of constant mean curvature, Ann. Univ. Ferrara - Sez. VII - Sc. Mat,, XLVIII (2002), pp. 189-217. | MR | Zbl

[17] F. Liang, An absolute gradient bound for nonparametric surfaces of constant mean curvature and the structure of generalized solutions for the constant mean curvature equation , Calc. Var. and P.D.E.'s, 7 (1998), pp. 99-123. | MR | Zbl

[18] F. Liang, Interpor gradient estimates for solutions to the mean curvature equation, Preprint.

[19] U. Massari - Miranda, Minimal Surfaces of Codimension One, North Holland Mathematics Studies 91, Elsevier Science Publ., Amsterdam, 1984. | MR | Zbl

[20] V. G. Maz'Ya, Sobolev Spaces, Springer Series in Soviet Mathematics, Springer-Verlag, 1095. | MR

[21] M. Miranda, Superfici cartesiane generalizzate ed insiemi di perimetro finito sui prodotti cartesiani, Ann. Sc. Norm. Sup. Pisa S. III, 18 (1964), pp. 515-542 | EuDML | Numdam | MR | Zbl

[22] M. Miranda, Superfici minime illimitate, Ann. Sc. Norm. Sup. Pisa S. IV, 4 (1977), pp. 313-322. | EuDML | Numdam | MR | Zbl

[23] M. Miranda, Sulle singolarietà eliminabili delle soluzioni dell'equazione delle superfici minime, Ann. Sc. Norm. Sup. Pisa S. IV, 4 (1977), pp. 129-132. | EuDML | Numdam | MR | Zbl

[24] J. B. Serrin, The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables, Phil. Trans. Roy. Soc. London A, 264 (1969), pp. 413-496. | MR | Zbl

[25] J. B. Serrin, The Dirichlet problems for surfaces of constant mean curvature, Proc. Lon. Math. Soc., (3) 21 (1970), pp. 361-384. | MR | Zbl

[26] 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., 69 (1972), pp. 821-823. | MR | Zbl

[27] N. S. Trudinger, Gradient estimates and mean curvature, Math. Z., 131 (1973), pp. 165-175. | EuDML | MR | Zbl

[28] N. S. Trudinger, Harnack inequalities for nonuniformly elliptiv divergence structure equations, Invent. Math., 64 (1981), pp. 517-531. | EuDML | MR | Zbl

[29] W. P. Ziemer, Weakly Differentiable Functions; Sobolev Spaces and Functions of Bounded Variations, Springer-Verlag, New York, 1989. | MR | Zbl