A THEOREM ON ESTIMATES FOR SOLUTIONS OF A CLASS OF NONLINEAR EQUATIONS IN FINITE-DIMENSIONAL SPACES

Abstract

The need to study boundary value problems for elliptic parabolic equations is dictated by
numerous practical applications in the theoretical study of the processes of hydrodynamics,
electrostatics, mechanics, heat conduction, elasticity theory, quantum physics.
In this paper, we obtain a theorem on an a priori estimate for the solution of nonlinear
equations in a finite-dimensional space. The work consists of two points. The first paragraph
contains the notation used and the formulation of the main result. In the second section, the
theorem is proved. The condition of the theorem is such that it can be used in the study of a
certain class of initial-boundary value problems to obtain an a priori estimate. This is the
meaning of this theorem.