Quantitative Rellich inequalities on Finsler-Hadamard manifolds

Kristály, Alexandru (author), Repovš, Dušan (author)

In this paper, we are dealing with quantitative Rellich inequalities on Finsler%Hadamard manifolds where the remainder terms are expressed by means of the flag curvature. By exploring various arguments from Finsler geometry and PDEs on manifolds, we show that more weighty curvature implies more powerful improvements in Rellich inequalities. The sharpness of the involved constants is also studied. Our results complement those of Yang, Su and Kong [Hardy inequalities on Riemannian manifolds with negative curvature, Commun. Contemp. Math. 16 (2014), Article ID: 1350043, 24 pp.].

• Language: English
• Keywords: Rellich inequality, Finsler-Hadamard manifold, Finsler-Laplace operato, curvature
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2016
• Number of pages: 17 str.
• Numbering: art. ID 1650020, no. 6
• PID: 20.500.12556/RUL-111089
• UDC: 514.7
• ISSN on article: 0219-1997
• DOI: 10.1142/S0219199716500206
• COBISS.SI-ID: 17651545
• Publication date in RUL: 23.09.2019

Record is a part of a journal

• Title: Communications in contemporary mathematics
• Shortened title: Commun. Contemp. Math.
• Publisher: World Scientific
• ISSN: 0219-1997
• COBISS.SI-ID: 9454425