Improved Caffarelli-Kohn-Nirenberg and trace inequalities for radial functions

Pablo L. De Nápoli; Irene Drelichman; Ricardo G. Durán

doi:10.3934/cpaa.2012.11.1629

Article Contents

2012, Volume 11, Issue 5: 1629-1642. Doi: 10.3934/cpaa.2012.11.1629

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Improved Caffarelli-Kohn-Nirenberg and trace inequalities for radial functions

1.
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires
2.
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Airess

Received: August 31, 2010

Revised: October 31, 2011

Published: August 2012

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Abstract

We show that Caffarelli-Kohn-Nirenberg first order interpolation inequalities as well as weighted trace inequalities in $\mathbb{R}^n \times \mathbb{R}_+$ admit a better range of power weights if we restrict ourselves to the space of radially symmetric functions.

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Mathematics Subject Classification: Primary: 26D10, 46E35; Secondary: 47G10.

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References

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