Translator Disclaimer
2012 Minimizing problems for the Hardy-Sobolev type inequality with the singularity on the boundary
Chang-Shou Lin, Hidemitsu Wadade
Tohoku Math. J. (2) 64(1): 79-103 (2012). DOI: 10.2748/tmj/1332767341

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.

Citation

Download Citation

Chang-Shou Lin. Hidemitsu Wadade. "Minimizing problems for the Hardy-Sobolev type inequality with the singularity on the boundary." Tohoku Math. J. (2) 64 (1) 79 - 103, 2012. https://doi.org/10.2748/tmj/1332767341

Information

Published: 2012
First available in Project Euclid: 26 March 2012

zbMATH: 1252.35146
MathSciNet: MR2911133
Digital Object Identifier: 10.2748/tmj/1332767341

Subjects:
Primary: 35J60
Secondary: 35B33

Rights: Copyright © 2012 Tohoku University

JOURNAL ARTICLE
25 PAGES


SHARE
Vol.64 • No. 1 • 2012
Back to Top