Abstract
It is proved that the problemdet(u xx)=f(x,u,u x)⩾Ν>0, is solvable in spaces\(C^{\kappa + 2 + \propto } (\bar \Omega ),\kappa \geqslant 2, 0< \propto< 1\), provided a natural connection between the curvature of the closed surface∂Ω and the growth of the functionf(x,u,p) in¦p¦ is valid.
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 131, pp. 72–79, 1983.
It is my pleasure mentioning that I have discussed the above material many times with O. A. Ladyzhenskaya and that for the clear understanding of all aspects of the problem I am deeply indebted to her for her remarks and advice.
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Ivochkina, N.M. Classical solvability of the Dirichlet problem for the Monge-Ampère equation. J Math Sci 30, 2287–2292 (1985). https://doi.org/10.1007/BF02105345
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DOI: https://doi.org/10.1007/BF02105345