Global behaviour and symmetry properties of singular solutions of nonlinear elliptic equations

Laurent Véron

Annales de la Faculté des sciences de Toulouse : Mathématiques (1984)

  • Volume: 6, Issue: 1, page 1-31
  • ISSN: 0240-2963

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Véron, Laurent. "Global behaviour and symmetry properties of singular solutions of nonlinear elliptic equations." Annales de la Faculté des sciences de Toulouse : Mathématiques 6.1 (1984): 1-31. <http://eudml.org/doc/73156>.

@article{Véron1984,
author = {Véron, Laurent},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {singular solutions; exterior domain; isotropic limit; spherical symmetric solutions; uniqueness; power like growth},
language = {eng},
number = {1},
pages = {1-31},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Global behaviour and symmetry properties of singular solutions of nonlinear elliptic equations},
url = {http://eudml.org/doc/73156},
volume = {6},
year = {1984},
}

TY - JOUR
AU - Véron, Laurent
TI - Global behaviour and symmetry properties of singular solutions of nonlinear elliptic equations
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1984
PB - UNIVERSITE PAUL SABATIER
VL - 6
IS - 1
SP - 1
EP - 31
LA - eng
KW - singular solutions; exterior domain; isotropic limit; spherical symmetric solutions; uniqueness; power like growth
UR - http://eudml.org/doc/73156
ER -

References

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  1. [1] Ph. Benilan, H. Brezis & M.G. Crandall. «A semilinear elliptic equation in L1(IRN)». Ann. Scuola Norm. Sup. Pisa, 2, 523-555 (1975). Zbl0314.35077
  2. [2] Ph. Benilan & H. Brezis. «Nonlinear problems related to the Thomas-Fermi equation». I n preparation. 
  3. [3] M. Berger, P. Gauduchon & E. Mazet. «Le spectre d'une variété reimannienne». Lecture Notes in Math., Springer-Verlag (1971). Zbl0223.53034
  4. [4] H. Brezis. «Equations d'évolution du second ordre associées à des opérateurs monotones». Israël J. Math., 12, 51-60 (1972). Zbl0248.47026MR317123
  5. [5] H. Brezis & E.H. Lieb. «Long range atomic potentials in Thomas-Fermitheory». Comm. Math. Phys., 65, 231-246 (1979). Zbl0416.35066
  6. [6] H. Brezis & L. Veron. «Removable singularities of some nonlinear elliptic equations». Arch. Rat. Mech. Anal., 75,1-6 (1980). Zbl0459.35032
  7. [7] B. Gidas. «Symmetry properties and isolated singularities of positive solutions of nonlinear elliptic equations.».Nonlinear Differential Equations in Engineering and Applied Sciences, ed. R.L. Sternberg, Marcel Dekker Inc. (1980). Zbl0444.35038MR577096
  8. [8] B. Gidas, Y.M. Ni & L. Nirenberg. «Symmetry and related properties via the maximum principle». Comm. Math. Phys., 68, 209-243 (1980). Zbl0425.35020
  9. [9] E. Hille. «Some aspects of the Thomas-Fermi equation». J. Analyse Math., 23, 147-170 (1970). Zbl0208.11501MR279376
  10. [10] T. Kato. «Schrödinger operators with singular potentials». Israël J. Math., 13, 135-148 (1973). Zbl0246.35025MR333833
  11. [11] E.H. Lieb & B. Simon. «The Thomas-Ferri theory of atoms, molecules and solids». Adv. in Math., 23, 22-116 (1977). Zbl0938.81568
  12. [12] A. Sommerfeld. «Asymptotishes integration der differential-gleichung des Thomas-Fermischen atoms». Z. für Phys., 78, 283-308 (1932). Zbl0005.23104
  13. [13] E.M. Stein. «Topics in harmonic analysis». Annals of Math.Studies Princeton Univ. Press (1970). Zbl0193.10502MR252961
  14. [14] L. Veron. «Comportement asymptotique des solutions d'équations elliptiques semi-linéaires dans IRN». Ann. Mat. Pura Appl., 127, 25-50 (1981). Zbl0467.35013MR633393
  15. [15] L. Veron. «Coercivité et propriétés régularisantes des semi-groupes non linéaires dans les espaces de Banach». Publ. Math. Univ. Besançon, 3, (1976). 
  16. [16] L. Veron. «Singular solutions of some nonlinear elliptic equations». Nonlinear Anal. T.M. & A., 5, 225-242 (1981). Zbl0457.35031
  17. [17] L. Veron. «Equations d'évolution semi-linéaires du second ordre dans L 1». Rev. Roum. Math. Pures et Appl., 27, 95-123 (1982). Zbl0489.35010MR658869

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