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

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.