Trudinger, Neil S. Gradient estimates and mean curvature. (English) Zbl 0253.53003 Math. Z. 131, 165-175 (1973). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 27 Documents MSC: 53A05 Surfaces in Euclidean and related spaces 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature 35Q05 Euler-Poisson-Darboux equations × Cite Format Result Cite Review PDF Full Text: DOI EuDML 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 · doi:10.1007/BF00281503 [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 · doi:10.2307/1969841 [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 · doi:10.1002/cpa.3160230409 [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 · doi:10.1112/plms/s3-21.2.361 [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 · doi:10.1017/S0004972700047262 [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 · doi:10.1073/pnas.69.4.821 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.