Geodesic
Two-weight Sobolev-Poincaré inequalities and Harnack inequality for a class of degenerate elliptic operators
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 5 (1994) no. 2, pp. 167-175

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

In this Note we prove a two-weight Sobolev-Poincaré inequality for the function spaces associated with a Grushin type operator. Conditions on the weights are formulated in terms of a strong \( A_{\infty} \)» weight with respect to the metric associated with the operator. Roughly speaking, the strong \( A_{\infty} \)» condition provides relationships between line and solid integrals of the weight. Then, this result is applied in order to prove Harnack's inequality for positive weak solutions of some degenerate elliptic equations. 
@article{RLIN_1994_9_5_2_a6,
     author = {Franchi, Bruno and Guti\'errez, Cristian E. and Wheeden, Richard L.},
     title = {Two-weight {Sobolev-Poincar\'e} inequalities and {Harnack} inequality for a class of degenerate elliptic operators},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {167--175},
     publisher = {mathdoc},
     volume = {Ser. 9, 5},
     number = {2},
     year = {1994},
     zbl = {0811.46023},
     mrnumber = {MR1292572},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_1994_9_5_2_a6/}
}
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Franchi, Bruno; Gutiérrez, Cristian E.; Wheeden, Richard L. Two-weight Sobolev-Poincaré inequalities and Harnack inequality for a class of degenerate elliptic operators. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 5 (1994) no. 2, pp. 167-175. http://geodesic.mathdoc.fr/item/RLIN_1994_9_5_2_a6/