Scientific seminar on the differential and functional differential equation on topic 鈥淥n nonlocal elliptic boundary value problems corresponding to infinite transformation groups鈥�
Speaker: Professor Savin Anton Yu., Mathematical Institute, RUDN University.
Topic: On nonlocal elliptic boundary value problems corresponding to infinite transformation groups.
In a number of problems of mathematical physics, noncommutative geometry, and the theory of differential equations, there arise nonlocal elliptic boundary value problems in which nonlocality is determined by shift operators corresponding to a certain group of diffeomorphisms. The most difficult case is when the diffeomorphisms do not preserve the domain in which the nonlocal problem is considered, and the group of diffeomorphisms is infinite. We discuss the formulation of such problems as bounded operators in Sobolev spaces, and provide criteria for the Fredholm solvability of problems. Specific examples are given.
The talk is based on joint work with A. Baldare, A.V. Boltachev, V.E. Nazaikinsky and E. Schroe.