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The regularity of convex regions with a metric that is regular in the Hölder classes. (English) Zbl 0386.53041

MSC:
53C45 Global surface theory (convex surfaces à la A. D. Aleksandrov)
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[1] A. V. Pogorelov, The Exterior Geometry of Convex Surfaces [in Russian], Nauka, Moscow (1969). · Zbl 0192.59403
[2] A. D. Aleksandrov, The Exterior Geometry of Convex Surfaces [in Russian], Gostekhizdat, Moscow (1948).
[3] I. Kh. Sabitov and S. Z. Shefel’, ?The connection between the order of smoothness of a surface and its metric,? Sibirsk. Matem. Zh.,17, No. 4, 916-925 (1976). · Zbl 0358.53015
[4] I. Ya. Bakel’man, A Geometric Method for Solving Elliptic Equations [in Russian], Nauka, Moscow (1975).
[5] E. Heinz, ?Über die Differentialungleichung 0<??rt-s2??<?,? Math. Z.,72, 107-126 (1959). · Zbl 0098.07202
[6] I. N. Vekua, Generalized Analytic Functions [in Russian], Fizmatgiz, Moscow (1959). · Zbl 0092.29703
[7] C. Miranda, Elliptic Partial Differential Equations [Russian translation], IL, Moscow (1957).
[8] L. I. Volkovyskii, Quasiconformal Mappings [in Russian], L’vovsk. Univ., L’vov (1954).
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