Weighted inequalities for the fractional Laplacian and the existence of extremals

Nápoli, Pablo L. De; Drelichman, Irene; Salort, Ariel

doi:10.1142/s0219199718500347

Cited by 3 publications

(1 citation statement)

References 15 publications

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“…However, we could not check the arguments on which the proof is based; see Yang & Wu [36,inequality (2.8)]; Yang [35, inequality (3.2)]. In this way, we believe that their results in these cases are still open problems; see De Nápoli, Drelichman & Salort [8].…”

Section: Model Problems and Main Resultsmentioning

confidence: 97%

A Fractional p-Laplacian Problem with Multiple Critical Hardy–Sobolev Nonlinearities

2020

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In this work, we study the existence of weak solution to the following quasi linear elliptic problem involving the fractional p-Laplacian operator, a Hardy potential and multiple critical Sobolev nonlinearities with singularities,To prove the existence of solution to the problem we have to formulate a refined version of the concentration-compactness principle and, as an independent result, we have to show that the extremals for the Sobolev inequality are attained.Mathematics Subject Classification (2010). Primary: 35J20, 35J92. Secondary: 35J10, 35B09, 35B38, 35B45.In the previous formula, by way of simplicity we introduced the notation: given 1 < m < +∞, we define the function J m : R → R by J m (t) = |t| m−2 t. Now we can define precisely the notion of weak solution to problem (1.7). We say that the function u ∈ D s,p (R N ) is a weak solution to problem (1.7) if

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Section: Model Problems and Main Resultsmentioning

confidence: 97%

A Fractional p-Laplacian Problem with Multiple Critical Hardy–Sobolev Nonlinearities

2020

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Existence of Extremals of Dunkl-Type Sobolev Inequality and of Stein–Weiss Inequality for Dunkl Riesz Potential

Adhikari

Anoop

Parui

2021

Complex Anal. Oper. Theory

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Stein-Weiss inequality in 𝐿¹ norm for vector fields

Nápoli¹,

Picon²

2023

Proc. Amer. Math. Soc.

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In this work, we investigate the limit case p = 1 p=1 of the classical Stein-Weiss inequality for the Riesz potential. Our main result is a characterization of this inequality for a special class of vector fields associated to cocanceling operators introduced by Van Schaftingen [J. Eur. Math. Soc. (JEMS) 15 (2013), pp. 877–921]. As application, we recover and improve some fractional inequalities associated to vector fields.

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Weighted inequalities for the fractional Laplacian and the existence of extremals

Cited by 3 publications

References 15 publications

A Fractional p-Laplacian Problem with Multiple Critical Hardy–Sobolev Nonlinearities

A Fractional p-Laplacian Problem with Multiple Critical Hardy–Sobolev Nonlinearities

Existence of Extremals of Dunkl-Type Sobolev Inequality and of Stein–Weiss Inequality for Dunkl Riesz Potential

Stein-Weiss inequality in 𝐿¹ norm for vector fields

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