Compact embedding of a degenerate Sobolev space and existence of entire solutions to a semilinear equation for a Grushin-type operator

Francesca Lascialfari; David Pardo

Rendiconti del Seminario Matematico della Università di Padova (2002)

  • Volume: 107, page 139-152
  • ISSN: 0041-8994

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Lascialfari, Francesca, and 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 107 (2002): 139-152. <http://eudml.org/doc/108574>.

@article{Lascialfari2002,
author = {Lascialfari, Francesca, Pardo, David},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
language = {eng},
pages = {139-152},
publisher = {Seminario Matematico of the University of Padua},
title = {Compact embedding of a degenerate Sobolev space and existence of entire solutions to a semilinear equation for a Grushin-type operator},
url = {http://eudml.org/doc/108574},
volume = {107},
year = {2002},
}

TY - JOUR
AU - Lascialfari, Francesca
AU - Pardo, David
TI - Compact embedding of a degenerate Sobolev space and existence of entire solutions to a semilinear equation for a Grushin-type operator
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2002
PB - Seminario Matematico of the University of Padua
VL - 107
SP - 139
EP - 152
LA - eng
UR - http://eudml.org/doc/108574
ER -

References

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  1. [1] H. BERESTYCKY - P. L. LIONS, Nonlinear Scalar Field Equations I, Arch. Rational Mech. Anal., 82 (1983), pp. 313-345. Zbl0533.35029MR695535
  2. [2] S. BIAGINI, Positive Solutions for a Semilinear Equation on the Heisenberg Group, Boll. UMI-B, 9 (7) (1995), pp. 901-918. Zbl0863.35036MR1369383
  3. [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. Zbl0589.46023MR764663
  4. [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. Zbl0685.35046MR963489
  5. [5] D. GILBARG - N. S. TRUDINGER, Elliptic Partial Differential Equations of Second Order, Second Edition, Springer Verlag, New York, 1983. Zbl0562.35001MR737190
  6. [6] B. KAWOHL, Rearrangements and Convexity of Level Sets in PDE, Lecture Notes in Mathematics 1150, Springer-Verlag, Berlin (1985). Zbl0593.35002MR810619
  7. [7] P. L. LIONS, Symétrie et Compacité dans les Espaces de Sobolev, J. Funct. Anal., 49 (1982), pp. 315-334. Zbl0501.46032MR683027
  8. [8] L. P. ROTSCHILD - E. M. STEIN, Hypoelliptic differential operators on nilpotent groups, Acta Math., 137 (1977), pp. 247-320. Zbl0346.35030MR436223
  9. [9] W. A. STRAUSS, Existence of Solitary Waves in Higher Dimensions, Comm. Math. Phys., 55 (1977), pp. 149-152. Zbl0356.35028MR454365
  10. [10] N. M. TRI, Critical Sobolev Exponent for Degenerate Elliptic Operators, Acta Math. Viet., 23 (1) (1998), pp. 83-94. Zbl0910.35060MR1628086
  11. [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). Zbl0913.35049MR1631852

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