scholarly journals Some rigidity results for Sobolev inequalities and related PDEs on Cartan-Hadamard manifolds

2021 ◽  
pp. 30
Author(s):  
Matteo Muratori ◽  
Nicola Soave
Keyword(s):  
Sobolev Inequalities ◽  
Hadamard Manifolds ◽  
Rigidity Results

scholarly journals Sharp Caffarelli–Kohn–Nirenberg inequalities on Riemannian manifolds: the influence of curvature

2021 ◽  
pp. 1-26
Author(s):  
Van Hoang Nguyen
Keyword(s):  
Euclidean Space ◽  
Riemannian Manifolds ◽  
Remainder Term ◽  
Sharp Constant ◽  
Hadamard Manifolds ◽  
Best Constant ◽  
Quantitative Version ◽  
Rigidity Results ◽  
Ckn Inequalities ◽  
Complete Riemannian Manifolds

We first establish a family of sharp Caffarelli–Kohn–Nirenberg type inequalities (shortly, sharp CKN inequalities) on the Euclidean spaces and then extend them to the setting of Cartan–Hadamard manifolds with the same best constant. The quantitative version of these inequalities also is proved by adding a non-negative remainder term in terms of the sectional curvature of manifolds. We next prove several rigidity results for complete Riemannian manifolds supporting the Caffarelli–Kohn–Nirenberg type inequalities with the same sharp constant as in the Euclidean space of the same dimension. Our results illustrate the influence of curvature to the sharp CKN inequalities on the Riemannian manifolds. They extend recent results of Kristály (J. Math. Pures Appl. 119 (2018), 326–346) to a larger class of the sharp CKN inequalities.

scholarly journals Sobolev inequalities with jointly concave weights on convex cones

2020 ◽  
Author(s):  
Zoltán M. Balogh ◽  
Cristian E. Gutiérrez ◽  
Alexandru Kristály
Keyword(s):  
Convex Cones ◽  
Sobolev Inequalities

scholarly journals Common Solution for a Finite Family of Equilibrium Problems, Quasi-Variational Inclusion Problems and Fixed Points on Hadamard Manifolds

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1161
Author(s):  
Jinhua Zhu ◽  
Jinfang Tang ◽  
Shih-sen Chang ◽  
Min Liu ◽  
Liangcai Zhao
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Finite Family ◽  
Variational Inclusion ◽  
Point Problem ◽  
Hadamard Manifolds ◽  
Inclusion Problems ◽  
Common Solution

In this paper, we introduce an iterative algorithm for finding a common solution of a finite family of the equilibrium problems, quasi-variational inclusion problems and fixed point problem on Hadamard manifolds. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in literature.

scholarly journals Sobolev Inequalities for Functions on Graphs

2021 ◽  
Vol 1804 (1) ◽  
pp. 012132
Author(s):  
Eman Samir Bhaya ◽  
Zainab Flaih
Keyword(s):  
Sobolev Inequalities

scholarly journals Two types of discrete Sobolev inequalities on a weighted Toeplitz graph

2016 ◽  
Vol 507 ◽  
pp. 344-355 ◽  
Author(s):  
Kazuo Takemura ◽  
Atsushi Nagai ◽  
Yoshinori Kametaka
Keyword(s):  
Sobolev Inequalities
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