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Abstract

The degenerating elliptic equations are one of the main equations of modern mechanics and theoretical physics. It is known that for the differential equations there are questions which can be carried to one of three categories: existence, uniqueness and qualitative behavior of decisions. In appendices mathematical methods are applied both to substantiation of adequacy of mathematical model, and to studying of character of course of real process. Therefore the important place in the theory of the linear and nonlinear elliptic
equations is taken up also by the third category of questions. In article the method of localization and a method of aprioristic estimates are used and the only strong solution of a task of Dirikhle is received at any    2 f x, y L .