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Nonlocal boundary value problems: index theory and semiclassical asymptotics

Project leader

Anton Savin

Department

S.M. Nikol’skii Mathematical Institute

Tags

nonlocal boundary value problems special domains Fredholm operators ellipticity of the index formula noncommutative geometry semiclassical asymptotics Lagrangian manifolds
Mathematics and Telecommunications Differential Equations
Functional-analytical methods for the study of boundary value problems for differential and functional differential equations with partial derivatives

Project leader

Vitalii Volpert

The main idea of the project: research of new classes of differential and functional-differential equations, inequalities and systems and the application of the obtained results to interdisciplinary research in mathematical models of physical and biological processes.

Department

S.M. Nikol’skii Mathematical Institute

Tags

reaction-diffusion equations Vlasov equation Liouville equation difference schemes identification problems for mixed partial differential equations elliptic functional differential equation nonlocal terms quasilinear equations differential-difference equations nonlocal elliptic operators Fredholm property index absolutely continuous spectrum singular spectrum scattering matrix trace formulas
Mathematics and Telecommunications Differential Equations
Non-commutative elliptic theory for the actions of groups on manifolds

Project leader

Anton Savin

The project aims to explore a number of interconnected challenges of modern theory of elliptic operators on manifolds with the actions of groups.

Department

S.M. Nikol’skii Mathematical Institute

Tags

elliptic theory Fredholm index noncommutative geometry quantized canonical transformations relative elliptic theory manifolds with singularities Sobolev problems algebraic index theorems
Mathematics and Telecommunications Differential Equations
Elliptic functional differential equations in bounded and unbounded domains

Project leader

Alexander Skubachevskii

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.

Department

S.M. Nikol’skii Mathematical Institute

Tags

elliptic problems functional-differential equations differential-difference equations Sobolev spaces weight spaces Kato hypothesis