Hardy-Sobolev Inequalities for Hessian Integrals

Nunzia Gavitone

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 3, page 951-967
  • ISSN: 0392-4041

Abstract

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Using appropriate symmetrization arguments, we prove the Hardy-Sobolev type inequalities for Hessian Integrals which extend the classical results, well known for Sobolev functions. For such inequalities the value of the best constant is given. Finally we give an improvement of these inequalities by adding a second term that, involves another singular weight which is a suitable negative power of log ⁡ ( | x | ) .

How to cite

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Gavitone, Nunzia. "Hardy-Sobolev Inequalities for Hessian Integrals." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 951-967. <http://eudml.org/doc/290419>.

@article{Gavitone2007,
abstract = {Using appropriate symmetrization arguments, we prove the Hardy-Sobolev type inequalities for Hessian Integrals which extend the classical results, well known for Sobolev functions. For such inequalities the value of the best constant is given. Finally we give an improvement of these inequalities by adding a second term that, involves another singular weight which is a suitable negative power of $\log (|x|)$.},
author = {Gavitone, Nunzia},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {951-967},
publisher = {Unione Matematica Italiana},
title = {Hardy-Sobolev Inequalities for Hessian Integrals},
url = {http://eudml.org/doc/290419},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Gavitone, Nunzia
TI - Hardy-Sobolev Inequalities for Hessian Integrals
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 951
EP - 967
AB - Using appropriate symmetrization arguments, we prove the Hardy-Sobolev type inequalities for Hessian Integrals which extend the classical results, well known for Sobolev functions. For such inequalities the value of the best constant is given. Finally we give an improvement of these inequalities by adding a second term that, involves another singular weight which is a suitable negative power of $\log (|x|)$.
LA - eng
UR - http://eudml.org/doc/290419
ER -

References

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