FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 1, PAGES 237-246

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

O. S. Rozanova

Abstract

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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 give the geometrical and geophysical applications. Namely, we concern 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 solution to the pressure-wind balance equation on a torus.

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Last modified: July 8, 2006