@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://www.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://www.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://www.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://www.numdam.org/item/RSMUP_2003__110__57_0/
[1] Una maggiorazione a priori relativa alle ipersuperifici minimali non parametriche, Arch. Rat. Mech. Anal., 32 (1969), pp. 255-267. | MR | Zbl
- - ,[2] Esistenza, unicità e regolarità nelle superfici di equilibrio nei capillari, Ann. Univ. Ferrera Sez. VII, 18 (1973), pp. 79-94. | MR | Zbl
,[3] Equilibrium Capillary Surfaces, Grundlehren der Mathem. Wiss. 284, Springer-Verlag, New York, 1986. | MR | Zbl
,[4] The inclination of an H-graph, Springer-Verlag Lecture Notes, 1340 (1973), pp. 381-394. | MR | Zbl
,[5] On non-parametric syrfaces of constant mean curvature, Ann. Sc. Norm. Sup. Pisa, 4 (1977), pp. 13-31. | Numdam | MR | Zbl
- ,[6] Some remarkable properties of H graphs, Mem. Diff. Equations Math. Physics, 12 (1997), pp. 57-61. | MR | Zbl
,[7] Existence, regularity, and boundary behavior of generalized surfaces of prescribed curvature, Math. Z., 139 (1974), pp. 173-198. | MR | Zbl
,[8] 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] On the regularity of solutions to Variational Problems in BV(V), Math. Z., 149 (1976), pp. 281-286. | MR | Zbl
,[10] Elliptic Partial Differential Equations of Second Order, 2nd Ed., Springer-Verlag, New York, 1983. | MR | Zbl
- ,[11] 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] Generalized solutions for the mean curvature equation, Pacific J. Math., 88 (1980), pp. 297-321. | MR | Zbl
,[13] Interior gradient estimates for surfaces z4f(x, y) of prescribed mean curvature, J. Diff. Geom. (1971), pp. 149-157. | MR | Zbl
,[14] 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] An absolute gradient bound for nonparametric surfaces of constant mean curvature, Indiana Univ. Math. J., 41(3) (1992), pp. 590-604. | MR | Zbl
,[16] 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] 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] Interpor gradient estimates for solutions to the mean curvature equation, Preprint.
,[19] Minimal Surfaces of Codimension One, North Holland Mathematics Studies 91, Elsevier Science Publ., Amsterdam, 1984. | MR | Zbl
,[20] Sobolev Spaces, Springer Series in Soviet Mathematics, Springer-Verlag, 1095. | MR
,[21] 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] Superfici minime illimitate, Ann. Sc. Norm. Sup. Pisa S. IV, 4 (1977), pp. 313-322. | EuDML | Numdam | MR | Zbl
,[23] 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] 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] The Dirichlet problems for surfaces of constant mean curvature, Proc. Lon. Math. Soc., (3) 21 (1970), pp. 361-384. | MR | Zbl
,[26] 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] Gradient estimates and mean curvature, Math. Z., 131 (1973), pp. 165-175. | EuDML | MR | Zbl
,[28] Harnack inequalities for nonuniformly elliptiv divergence structure equations, Invent. Math., 64 (1981), pp. 517-531. | EuDML | MR | Zbl
,[29] Weakly Differentiable Functions; Sobolev Spaces and Functions of Bounded Variations, Springer-Verlag, New York, 1989. | MR | Zbl
,