Rellich inequalities for polyharmonic operators in plane domains. (March 2018) - Avkhadiev, F. G.
Abstract: Functionals whose values are defined as sharp constants in Rellich inequalities are investigated for polyharmonic operators in plane domains. The weight function is taken to be a power of the distance of a point to the boundary of the domain. Estimates are obtained for arbitrary domains, as is a test for these constants to be positive, and precise values are found for convex domains and for domains close to convex in a certain sense. The case when the weight function is taken to be a power of the coefficient in the Poincaré metric is also treated. Bibliography: 28 titles.