EVENT DETAILS AND ABSTRACT

Title: Elliptic Functional Differential Equations and Applications
Speaker: Professor Alexander Skubachevskii
Speaker Info: Peoples' Friendship University of Russia
Brief Description:
Special Note: Special Time
Abstract:

Elliptic functional differential equations have some new astonishing properties. For example, smoothness of generalized solutions can be violated inside domain even for infinitely differentiable right hand sides. We consider the necessary and sufficient conditions for correctness of the Garding type inequality. We shall also study spectral properties of strongly elliptic differential-difference equations. Smoothness of generalized solutions of elliptic differential-difference equations is preserved only in some subdomains. Moreover, arbitrary small coefficients in difference operators can lead to violation of smoothness on the boundaries of neighboring subdomains and near the set of conjugation points. We shall consider applications to the theory of laser beams. Elliptic differential-difference equations are closely connected with so-called nonlocal elliptic boundary value problems.