Compact embedding of a degenerate Sobolev space and existence of entire solutions to a semilinear equation for a Grushin-type operator
Lascialfari, Francesca ; Pardo, David
Rendiconti del Seminario Matematico della Università di Padova, Tome 108 (2002), p. 139-152 / Harvested from Numdam
Publié le : 2002-01-01
@article{RSMUP_2002__107__139_0,
     author = {Lascialfari, Francesca and Pardo, David},
     title = {Compact embedding of a degenerate Sobolev space and existence of entire solutions to a semilinear equation for a Grushin-type operator},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {108},
     year = {2002},
     pages = {139-152},
     mrnumber = {1926206},
     zbl = {1072.35073},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_2002__107__139_0}
}
Lascialfari, Francesca; Pardo, David. Compact embedding of a degenerate Sobolev space and existence of entire solutions to a semilinear equation for a Grushin-type operator. Rendiconti del Seminario Matematico della Università di Padova, Tome 108 (2002) pp. 139-152. http://gdmltest.u-ga.fr/item/RSMUP_2002__107__139_0/

[1] H. Berestycky - P. L. Lions, Nonlinear Scalar Field Equations I, Arch. Rational Mech. Anal., 82 (1983), pp. 313-345. | MR 695535 | Zbl 0533.35029

[2] S. Biagini, Positive Solutions for a Semilinear Equation on the Heisenberg Group, Boll. UMI-B, 9 (7) (1995), pp. 901-918. | MR 1369383 | Zbl 0863.35036

[3] B. Franchi - E. Lanconelli, An Embedding Theorem for Sobolev Spaces related to Non-Smooth Vector Fields and Harnack Inequality, Comm. in Part. Diff. Eq., 9 (13) (1984), pp. 1237-1264. | MR 764663 | Zbl 0589.46023

[4] B. Franchi - R. Serapioni, Pointwise Estimates for a Class of Strongly Degenerate Elliptic Operators: a Geometrical Approach, Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV Ser. 14, N. 4 (1987), pp. 527-568. | Numdam | MR 963489 | Zbl 0685.35046

[5] D. Gilbarg - N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Second Edition, Springer Verlag, New York, 1983. | MR 737190 | Zbl 0562.35001

[6] B. Kawohl, Rearrangements and Convexity of Level Sets in PDE, Lecture Notes in Mathematics 1150, Springer-Verlag, Berlin (1985). | MR 810619 | Zbl 0593.35002

[7] P. L. Lions, Symétrie et Compacité dans les Espaces de Sobolev, J. Funct. Anal., 49 (1982), pp. 315-334. | MR 683027 | Zbl 0501.46032

[8] L. P. Rotschild - E. M. Stein, Hypoelliptic differential operators on nilpotent groups, Acta Math., 137 (1977), pp. 247-320. | MR 436223 | Zbl 0346.35030

[9] W. A. Strauss, Existence of Solitary Waves in Higher Dimensions, Comm. Math. Phys., 55 (1977), pp. 149-152. | MR 454365 | Zbl 0356.35028

[10] N. M. Tri, Critical Sobolev Exponent for Degenerate Elliptic Operators, Acta Math. Viet., 23 (1) (1998), pp. 83-94. | MR 1628086 | Zbl 0910.35060

[11] N. M. Tri, On Grushin's Equation, Math. Notes, 63 (1) (1998), pp. 84-93 (Transl. from Mmat. Zametki, 63 (1) (1998), pp. 95-105). | MR 1631852 | Zbl 0913.35049