The hyperbolic Monge-Ampere equation: classical solutions on the whole plane

TL;DR

This paper investigates the hyperbolic Monge-Ampere equation, establishing conditions under which a unique classical solution exists globally on the entire plane, considering the most general form with variable coefficients.

Contribution

It provides the first comprehensive set of sufficient conditions for the existence of global classical solutions to the general hyperbolic Monge-Ampere equation.

Findings

Sufficient conditions for global C^3-solutions are formulated.

The equation's most general form with arbitrary coefficient functions is analyzed.

Existence and uniqueness of solutions on the whole plane are established.

Abstract

The Cauchy problem for the hyperbolic Monge-Ampere equation is considered. The equation has the most general form. Coefficients are arbitrary functions depending on two independent variables, unknown function, and first order derivatives. Sufficient conditions on the existence of a (unique) C^3-solution on the whole plain are formulated.