A Caffarelli–Kohn–Nirenberg type inequality on Riemannian manifolds

Bozhkov, Yuri

doi:10.1016/j.aml.2010.05.004

Cited by 7 publications

(7 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this last section, we first state the Hardy type inequality. The proof follows easily combining the ideas in [7] and [23]. It is important to note that, the inequality in the Euclidean case can be recovered with h(x) = x.…”

Section: Appendixmentioning

confidence: 88%

“…Concerning the Sobolev inequality in its weighted version, the distance function is a commonly used weight function, see [19,25], but it is not a consensus. In a different and interesting direction, it was used in [7] the existence of a conformal Killing vector field h (see the definition below) on a complete n-manifold M , n ≥ 3, to prove the following inequality…”

Section: The Riemannian Casementioning

confidence: 99%

See 1 more Smart Citation

A scaling approach to Caffarelli-Kohn-Nirenberg inequality

Bazan,

Neves

2013

Preprint

View full text Add to dashboard Cite

We consider the general Caffarelli-Kohn-Nirenberg inequality in the Euclidean and Remannian setting. From a new parameter introduced, the proof of the former case, follows by simple interpolation arguments and Hölder's inequality. Moreover, the ranges of this convenient parameter completely characterize the inequality. Secondly, the same technics are used to study the Caffarelli-Kohn-Nirenberg inequality in the Riemannian case.

show abstract

Section: Appendixmentioning

confidence: 88%

Section: The Riemannian Casementioning

confidence: 99%

A scaling approach to Caffarelli-Kohn-Nirenberg inequality

Bazan,

Neves

2013

Preprint

View full text Add to dashboard Cite

show abstract

“…For further applications, e. g. Hardy and Caffarelli-Kohn-Nirenberg type inequalities, see [6] and [2].…”

Section: Be Two Given Functions and Letmentioning

confidence: 99%

Conformal Killing Vector Fields and Rellich Type Identities on Riemannian Manifolds, II

Bozhkov

Mitidieri

2011

Mediterr. J. Math.

Self Cite

View full text Add to dashboard Cite

We propose a general Noetherian approach to Rellich integral identities. Using this method we obtain a higher order Rellich type identity involving the polyharmonic operator on Riemannian manifolds admitting homothetic transformations. Then we prove a biharmonic Rellich identity in a more general context. We also establish a nonexistence result for semilinear systems involving biharmonic operators.Mathematics Subject Classification (2010). 35J50, 35J20, 35J60.

show abstract

“…where w(x) is a non-negative function satisfying inf w(x) = 0, on a Riemannian Manifold with Riemannain metric g, for example see [1,2,4,16]. Degenerate differential operators involving a non-negative weight which appear in singular quasilinear elliptic equations have been studied by some authors in Euclidean and Riemannian manifolds forms.…”

Section: Introductionmentioning

confidence: 99%