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.

Location: http://mech.math.msu.su/~fpm/eng/k06/k061/k06108h.htm

Last modified: July 8, 2006