Tohoku Mathematical Journal

Minimizing problems for the Hardy-Sobolev type inequality with the singularity on the boundary

Chang-Shou Lin and Hidemitsu Wadade

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Abstract

In this paper, we consider the existence of minimizers of the Hardy-Sobolev type variational problem. Recently, Ghoussoub and Robert proved that the Hardy-Sobolev best constant admits its minimizers provided the bounded smooth domain has the negative mean curvature at the origin on the boundary. We generalize their results by using the idea of Brézis and Nirenberg, and as a consequence, we shall prove the existence of positive solutions to the elliptic equation involving two different kinds of Hardy-Sobolev critical exponents.

Article information

Source
Tohoku Math. J. (2), Volume 64, Number 1 (2012), 79-103.

Dates
First available in Project Euclid: 26 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1332767341

Digital Object Identifier
doi:10.2748/tmj/1332767341

Mathematical Reviews number (MathSciNet)
MR2911133

Zentralblatt MATH identifier
1252.35146

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B33: Critical exponents

Keywords
Minimizing problem Hardy-Sobolev inequality negative mean curvature

Citation

Lin, Chang-Shou; Wadade, Hidemitsu. Minimizing problems for the Hardy-Sobolev type inequality with the singularity on the boundary. Tohoku Math. J. (2) 64 (2012), no. 1, 79--103. doi:10.2748/tmj/1332767341. https://projecteuclid.org/euclid.tmj/1332767341


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