Svetlana Ivanovna Prokofyeva
The St. Petersburg State University of Architecture and Civil Engineering,
math. dept. Assoc.Prof. PhD
Galina Vladimirovna Yakunina
The St. Petersburg State University of Architecture and Civil Engineering,
math. dept. Assoc.Prof. PhD
The article reconsiders the role of ellipticity notion for nonlinear differential second order equations. It demonstrates that the positive monotone cone is a natural set of solvability and uniqueness of the solution of Dirichlet problem for these equations. The article gives the example of equations that are elliptic in the cone as well as out of the cone. This equation has a solution both in the cone and out of the cone. These solutions are different.