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On domains of regularity of the solutions of some special classes of Monge-Ampère-type equations

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Abstract

We present several results on estimates from above of the regularity domains for special classes of solutions to Monge-Ampère-type equations (in particular, periodic at least in one variable). Also, we present some geometrical and geophysical applications. Namely, we are concerned with the problem on dimensions of a single-valued projection on a plane of a surface with separated-from-zero negative Gaussian curvature and discuss the existence or nonexistence of a solution to the pressure-wind balance equation on a torus.

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Authors and Affiliations

  1. Moscow State University, Russia

    O. S. Rozanova

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  1. O. S. Rozanova
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 1, pp. 237–246, 2006.

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Rozanova, O.S. On domains of regularity of the solutions of some special classes of Monge-Ampère-type equations. J Math Sci 149, 1021–1027 (2008). https://doi.org/10.1007/s10958-008-0040-1

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  • DOI: https://doi.org/10.1007/s10958-008-0040-1

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