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Gradient estimates and mean curvature. (English) Zbl 0253.53003

MSC:
53A05 Surfaces in Euclidean and related spaces
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
35Q05 Euler-Poisson-Darboux equations
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References:
[1] Bombieri, E.: Theory of minimal surfaces and a counterexample to the Bernstein conjecture in high dimensions. Lecture notes New York: Courant Institute of Mathematical Sciences 1970.
[2] Bombieri, E., Giusti, E.: Local estimates for the gradient of non-parametric surfaces of prescribed mean curvature. Commun. pure appl. Math., to appear. · Zbl 0266.53042
[3] Bombieri, E., De Giorgi, E., Miranda, M.: Una maggiorazione a priori relative alle ipersuperfici minimali non parametriche. Arch. rat. Mech. Analysis32, 255-269 (1969). · Zbl 0184.32803
[4] Courant, R., Hilbert, D.: Methods of mathematical physics. Vol. II: Partial Differential Equations, New York: John Wiley 1962. · Zbl 0099.29504
[5] Finn, R.: On equations of minimal surface type. Ann. of Math.60 397-416 (1954). · Zbl 0058.32501
[6] Heinz, E.: Interior gradient estimates for surfacesz=f(x,y) with prescribed mean curvature. J. diff. Geometry5, 149-157 (1971). · Zbl 0212.44001
[7] Ladyzhenskaya, O. A., Ural’tseva, N. N.: Local estimates for the gradients of solutions of nonuniformly elliptic and parabolic equations. Commun. pure appl. Math.23, 677-703 (1970). · Zbl 0193.07202
[8] Miranda, M.: Una maggiorazione integrale per le curvature delle ipersuperfici minimali. Rend. Sem. mat. Univ. Padova38, 91-102 (1967). · Zbl 0175.11803
[9] Serrin, J.: The Dirichlet problem for surfaces of constant mean curvature. Proc. London math. Soc. III. Ser.,21, 361-384 (1970). · Zbl 0199.16604
[10] Simon, L.M.: Interior gradient bounds for non-uniformly elliptic partial differential equations of divergence form. Doctoral dissertation, University of Adelaide, December 1971.
[11] Trudinger, N.S.: On the analyticity of generalized minimal surfaces. Bull. Austral. math. Soc.5, 315-320 (1971). · Zbl 0231.35014
[12] Trudinger, N.S.: A new proof of the interior gradient bound for the minimal surface equation inn dimensions. Proc. nat. Acad. Sci. USA,69, 821-823, (1972). · Zbl 0231.53007
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