Hardy-type inequalities related to degenerate elliptic differential operators

Lorenzo D’Ambrosio[1]

  • [1] Dipartimento di Matematica Via E. Orabona, 4 I-70125 Bari, Italy

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2005)

  • Volume: 4, Issue: 3, page 451-486
  • ISSN: 0391-173X

Abstract

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We prove some Hardy-type inequalities related to quasilinear second-order degenerate elliptic differential operators L p u : = - L * ( L u p - 2 L u ) . If φ is a positive weight such that - L p φ 0 , then the Hardy-type inequalityholds. We find an explicit value of the constant involved, which, in most cases, results optimal. As particular case we derive Hardy inequalities for subelliptic operators on Carnot Groups.

How to cite

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D’Ambrosio, Lorenzo. "Hardy-type inequalities related to degenerate elliptic differential operators." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 4.3 (2005): 451-486. <http://eudml.org/doc/84567>.

@article{D2005,
abstract = {We prove some Hardy-type inequalities related to quasilinear second-order degenerate elliptic differential operators $L_pu:=-\nabla _L^*(\left|\nabla _Lu\right|^\{p-2\}\nabla _Lu)$. If $\phi $ is a positive weight such that $-L_p\phi \ge 0$, then the Hardy-type inequalityholds. We find an explicit value of the constant involved, which, in most cases, results optimal. As particular case we derive Hardy inequalities for subelliptic operators on Carnot Groups.},
affiliation = {Dipartimento di Matematica Via E. Orabona, 4 I-70125 Bari, Italy},
author = {D’Ambrosio, Lorenzo},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {3},
pages = {451-486},
publisher = {Scuola Normale Superiore, Pisa},
title = {Hardy-type inequalities related to degenerate elliptic differential operators},
url = {http://eudml.org/doc/84567},
volume = {4},
year = {2005},
}

TY - JOUR
AU - D’Ambrosio, Lorenzo
TI - Hardy-type inequalities related to degenerate elliptic differential operators
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2005
PB - Scuola Normale Superiore, Pisa
VL - 4
IS - 3
SP - 451
EP - 486
AB - We prove some Hardy-type inequalities related to quasilinear second-order degenerate elliptic differential operators $L_pu:=-\nabla _L^*(\left|\nabla _Lu\right|^{p-2}\nabla _Lu)$. If $\phi $ is a positive weight such that $-L_p\phi \ge 0$, then the Hardy-type inequalityholds. We find an explicit value of the constant involved, which, in most cases, results optimal. As particular case we derive Hardy inequalities for subelliptic operators on Carnot Groups.
LA - eng
UR - http://eudml.org/doc/84567
ER -

References

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