Abstract
One proves that a priori boundedness of the norm
of the solution of the problem det(Uxx)=f(x,u,ux)≥>ν>0,u¦∂Ω=0. The magnitudes of the exponentsγ,δ(γ) depends on whether the arguments u p occur or not in f (x,u,p).
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Literature cited
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 125, pp. 74–90, 1983.
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Ivochkina, N.M. A priori estimates of the solution of the dirichlet problem for the Monge-ampére equation in weight spaces. J Math Sci 26, 2349–2359 (1984). https://doi.org/10.1007/BF01680015
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DOI: https://doi.org/10.1007/BF01680015