Rellich inequalities for polyharmonic operators in plane domains. (March 2018)

• Record Type: Journal Article
• Authors: Avkhadiev, F. G.
• Is Part Of: Sbornik. Volume 209:Number 3(2018)
• Page Start: 292
• Page End: 319
• Publication Date: 2018-03
• Subjects: 35A23; Rellich inequality -- polyharmonic operator -- uniformly perfect set -- Poincaré metric.; Mathematics -- Periodicals; 510.5
• DOI: 10.1070/SM8739
• Languages: English
• ISSNs: 1064-5616

Abstract

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.