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The project analyzes boundary value problems for elliptic functional-differential equations in bounded domains and half-space, as well as elliptic functional-differential equations in the entire space R^n.

Project leader

Anton Savin

The main goal of the project is to create a noncommutative elliptic theory for a new class of operators associated with the representation of a group by quantized canonical transformations on different varieties.

Project leader

Vladimir Filippov

To study linear elliptic differential-difference equations, symmetrized matrices corresponding to difference operators are used, while the skew-symmetric component does not violate the strong ellipticity of the linear operator and the smoothness properties of generalized solutions. Previously, the solvability criteria for nonlinear elliptic differential-difference equations were proposed, in which the difference operators are described by symmetric matrices. It was shown that, unlike the linear case for nonlinear problems, the skew-symmetric part affects ellipticity. In this project, we propose to use previously developed methods to study nonlinear elliptic problems with difference operators, which correspond to triangular matrices.