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Seminar on Complex Analysis (Gonchar Seminar)
November 14, 2016 17:00, Moscow, Steklov Mathematical Institute, Room 411 (8 Gubkina)
 


Rellich type inequalities for polyharmonic operators in plane domains

F. G. Avkhadiev

Institute of Mathematics and Mechanics, Kazan (Volga Region) Federal University

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Abstract: For polyharmonic operators we study Rellich type inequalities in plane domains. We prove that these inequalities are pithy if and only if the boundary of the domain is a uniformly perfect set. We prove that the constants in these inequalities are determined exactly for convex domains as well as for domains that are close to convex in certain sense. Also, it is investigated new versions of the main inequality, when weight functions are powers of the coefficient of the Poincaré metric.

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