General Gagliardo Inequality and Applications to Weighted Sobolev Spaces

Antonio Avantaggiati; Paola Loreti

Bollettino dell'Unione Matematica Italiana (2009)

  • Volume: 2, Issue: 3, page 623-633
  • ISSN: 0392-4041

Abstract

top
In this paper we obtain a more general inequality with respect to a well known inequality due to Gagliardo (see [4], [5]). The inequality contained in [4], [5] has been extended to weighted spaces, obtained as cartesian product of measurable spaces. As application, we obtain a first order weighted Sobolev inequality. This generalize a previous result obtained in [2].

How to cite

top

Avantaggiati, Antonio, and Loreti, Paola. "General Gagliardo Inequality and Applications to Weighted Sobolev Spaces." Bollettino dell'Unione Matematica Italiana 2.3 (2009): 623-633. <http://eudml.org/doc/290565>.

@article{Avantaggiati2009,
abstract = {In this paper we obtain a more general inequality with respect to a well known inequality due to Gagliardo (see [4], [5]). The inequality contained in [4], [5] has been extended to weighted spaces, obtained as cartesian product of measurable spaces. As application, we obtain a first order weighted Sobolev inequality. This generalize a previous result obtained in [2].},
author = {Avantaggiati, Antonio, Loreti, Paola},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {623-633},
publisher = {Unione Matematica Italiana},
title = {General Gagliardo Inequality and Applications to Weighted Sobolev Spaces},
url = {http://eudml.org/doc/290565},
volume = {2},
year = {2009},
}

TY - JOUR
AU - Avantaggiati, Antonio
AU - Loreti, Paola
TI - General Gagliardo Inequality and Applications to Weighted Sobolev Spaces
JO - Bollettino dell'Unione Matematica Italiana
DA - 2009/10//
PB - Unione Matematica Italiana
VL - 2
IS - 3
SP - 623
EP - 633
AB - In this paper we obtain a more general inequality with respect to a well known inequality due to Gagliardo (see [4], [5]). The inequality contained in [4], [5] has been extended to weighted spaces, obtained as cartesian product of measurable spaces. As application, we obtain a first order weighted Sobolev inequality. This generalize a previous result obtained in [2].
LA - eng
UR - http://eudml.org/doc/290565
ER -

References

top
  1. ADAMS, R. A., Sobolev Spaces, Academic Press (1975). MR450957
  2. AVANTAGGIATI, A. - LORETI, P., Gagliardo type inequality and application, Collana Scientifica di Ateneo, Università di Salerno, in ricordo di Vittorio Cafagna. 
  3. AVANTAGGIATI, A. - LORETI, P., Idempotent aspects of Hopf-Lax type formulas, Proceedings of the International Conference on Tropical and Idempotent Mathematics, Edited by G. L. Litvinov and S. N. Sergeev, Contemporary Mathematics, American Mathematical Society, 495 (2009), 103-114. Zbl1180.37117MR2581515DOI10.1090/conm/495/09693
  4. GAGLIARDO, E., Proprietà di alcune classi di funzioni di più variabili, Ricerche di Matematica, 7 (1958), 102-137. MR102740
  5. GAGLIARDO, E., Ulteriori proprietà di alcune classi di funzioni di più variabili, Ricerche di Matematica, 8 (1959), 24-51. MR109295
  6. CRAIG EVANS, L., Partial Differential Equations, Graduate Studies in Mathematics, American Mathematical Society, 1998. MR1625845
  7. TROISI, M., Teoremi di immersione per spazi di Sobolev non isotropi, Ricerche di Matematica, Vol. XVIII (1969), 1-24. MR415302
  8. TROISI, M., Teoremi di inclusione negli spazi di Sobolev con peso, Ricerche di Matematica, Vol. XVIII (1969), 49-74. MR412802

NotesEmbed ?

top

You must be logged in to post comments.