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Radial fractional Laplace operators and Hessian inequalities
- Source :
-
Journal of Differential Equations . Jul2012, Vol. 253 Issue 1, p244-272. 29p. - Publication Year :
- 2012
-
Abstract
- Abstract: In this paper we deduce a formula for the fractional Laplace operator on radially symmetric functions useful for some applications. We give a criterion of subharmonicity associated with , and apply it to a problem related to the Hessian inequality of Sobolev type: where is the k-Hessian operator on , , under some restrictions on a k-convex function u. In particular, we show that the class of u for which the above inequality was established in Ferrari et al. contains the extremal functions for the Hessian Sobolev inequality of X.-J. Wang (1994) . This is proved using logarithmic convexity of the Gaussian ratio of hypergeometric functions which might be of independent interest. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 253
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 74643439
- Full Text :
- https://doi.org/10.1016/j.jde.2012.03.024