Find out how to access previewonly content
Date:
07 Nov 2012
On the Optimality of the Assumptions Used to Prove the Existence and Symmetry of Minimizers of Some Fractional Constrained Variational Problems
 Hichem Hajaiej
 … show all 1 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
In this paper, we discuss the optimality of the assumptions used, in a previous paper, to prove existence and symmetry of minimizers of the fractional constrained variational problem:
$$\inf \;\left\{\frac{1}{2}
\int\nabla_s u^2  \int F(x, u):\;u\in H^s (\mathbb{R}^N) \mbox{ and }
\int u^2 = c^2\right\},$$

There is no minimizer at all.

The infimum is achieved but no minimizer is radial.

For some values of c there is no minimizer. For large values, the minimizer is radial and radially decreasing.
 Title
 On the Optimality of the Assumptions Used to Prove the Existence and Symmetry of Minimizers of Some Fractional Constrained Variational Problems
 Journal

Annales Henri Poincaré
Volume 14, Issue 5 , pp 14251433
 Cover Date
 201307
 DOI
 10.1007/s000230120212x
 Print ISSN
 14240637
 Online ISSN
 14240661
 Publisher
 SP Birkhäuser Verlag Basel
 Additional Links
 Topics
 Authors

 Hichem Hajaiej ^{(1)}
 Author Affiliations

 1. Department of Mathematics, King Saud University, 11451, Riyadh, Kingdom of Saudi Arabia