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September 2020 A minimization problem involving a fractional Hardy–Sobolev type inequality
Antonella Ritorto
Illinois J. Math. 64(3): 305-317 (September 2020). DOI: 10.1215/00192082-8591568

Abstract

In this work, we obtain existence of nontrivial solutions to a minimization problem involving a fractional Hardy–Sobolev type inequality in the case of inner singularity. Precisely, for λ > 0 , we analyze the attainability of the optimal constant μ α , λ ( Ω ) : = inf  { [ u ] s , Ω 2 + λ Ω | u | 2 d x : u H s ( Ω ) , Ω | u ( x ) | 2 s , α | x | α d x = 1 } , where 0 < s < 1 , n > 4 s , 0 α < 2 s , 2 s , α = 2 ( n α ) n 2 s , and Ω R n is a bounded domain such that 0 Ω .

Citation

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Antonella Ritorto. "A minimization problem involving a fractional Hardy–Sobolev type inequality." Illinois J. Math. 64 (3) 305 - 317, September 2020. https://doi.org/10.1215/00192082-8591568

Information

Received: 9 October 2019; Revised: 2 April 2020; Published: September 2020
First available in Project Euclid: 1 July 2020

zbMATH: 07235505
MathSciNet: MR4132593
Digital Object Identifier: 10.1215/00192082-8591568

Subjects:
Primary: 35R11
Secondary: 35R34

Rights: Copyright © 2020 University of Illinois at Urbana-Champaign

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Vol.64 • No. 3 • September 2020
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