ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ
ΤΜΗΜΑ ΜΑΘΗΜΑΤΙΚΩΝ
ΣΕΜΙΝΑΡΙΟ σε Elliptic differential-difference equations
Τρίτη 12 Φεβρουαρίου 2018, Αίθουσα Μ2
18.15 Leonid Rossovskii, Πανεπιστήμιο Φιλίας των Λαών (RUDN), Μόσχα
Τίτλος: Elliptic differential-difference equations and applications
Περίληψη: Boundary-value problems are considered for strongly elliptic differential-difference equations in bounded domains. In contrast to the case of elliptic differential equations, smoothness of generalized solutions of such problems can be violated in the interior of the domain and may be preserved only in some subdomains, and the symbol of a self-adjoint semibounded functional-differential operator can change sign.
Both necessary and sufficient conditions are obtained for the Gårding-type inequality in algebraic form. Spectral properties of strongly elliptic functional-differential operators are studied, and theorems are proved on smoothness of generalized solutions in subdomains. Applications of these results are found to the theory of nonlocal elliptic problems, to the Kato square-root problem, to elasticity theory, and to problems in non-linear optics.