Isotropic singularities of solutions of nonlinear elliptic inequalities

Yves Richard; Laurent Veron

Annales de l'I.H.P. Analyse non linéaire (1989)

  • Volume: 6, Issue: 1, page 37-72
  • ISSN: 0294-1449

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Richard, Yves, and Veron, Laurent. "Isotropic singularities of solutions of nonlinear elliptic inequalities." Annales de l'I.H.P. Analyse non linéaire 6.1 (1989): 37-72. <http://eudml.org/doc/78168>.

@article{Richard1989,
author = {Richard, Yves, Veron, Laurent},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {fundamental solutions; weak singularities existence},
language = {eng},
number = {1},
pages = {37-72},
publisher = {Gauthier-Villars},
title = {Isotropic singularities of solutions of nonlinear elliptic inequalities},
url = {http://eudml.org/doc/78168},
volume = {6},
year = {1989},
}

TY - JOUR
AU - Richard, Yves
AU - Veron, Laurent
TI - Isotropic singularities of solutions of nonlinear elliptic inequalities
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1989
PB - Gauthier-Villars
VL - 6
IS - 1
SP - 37
EP - 72
LA - eng
KW - fundamental solutions; weak singularities existence
UR - http://eudml.org/doc/78168
ER -

References

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  1. [1] P. Aviles, On Isolated Singularities in Some Nonlinear Partial Differential Equations, Indiana Univ. Math. J., Vol. 32, 1983, pp. 773-791. Zbl0548.35042MR711867
  2. [2] P. Aviles, Local Behaviour of Solutions of Some Elliptic Equations, Com. Math. Phys., Vol. 108, 1987, pp. 177-192. Zbl0617.35040MR875297
  3. [3] Ph. Benilanand H. Brezis, Nonlinear Problems Related to the Thomas-Fermi Equation(in preparation). See also H. Brezis, Some Variational Problems of the Thomas-Fermi Type, in Variational Inequalities and Complementary Conditions, R. W. COTTLE, F. GIANESSI and J. L. LIONS, Eds., Wiley-Interscience, 1990, pp. 53–73. Zbl0643.35108
  4. [4] H. Brezis and E.T. Lieb, Long Range Atomic Potentials in Thomas-Fermi Theory,Com. Math. Phys., Vol. 65, 1980, pp. 231–246. Zbl0416.35066MR530151
  5. [5] H. Brezis and P.L. Lions, A note on Isolated Singularities for Linear Elliptic Equations, Mathematical Analysis and Applications, Vol 7A, 1981, pp. 263–266. Zbl0468.35036MR634242
  6. [6] H. Brezis and L. Oswald, Singular Solutions for Some Semilinear Elliptic Equations, Arch. Rat. Mech. Anal. (to appear). Zbl0635.35035MR888452
  7. [7] R.H. Fowler, Further Studies in Emden's and Similar Differential Equations, Quart. J. Math., Vol. 2, 1931, pp. 259–288. Zbl0003.23502
  8. [8] B. Gidas and J. Spruck, Global and Local Behaviour of Positive Solutions of Nonlinear Elliptic Equations, Comm. Pure Appl. Math., Vol 34, 1980, pp. 525–598. Zbl0465.35003MR615628
  9. [9] D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1983. Zbl0562.35001MR737190
  10. [10] M. Guedda and L. Veron, Local and Global Properties of Solutions of Quasilinear Elliptic Equations, J. Diff. Equ., Vol. 75, 1988. Zbl0661.35029MR964617
  11. [11] P.L. Lions, Isolated Singularities in Semilinear Problems, J. Diff. Equ. Vol. 38, 1980, pp. 441–550. Zbl0458.35033MR605060
  12. [12] W.M. Ni and J. Serrin, Nonexistence Theorems for Singular Solutions of Quasilinear Partial Differential Equations, Comm. Pure Applied Math., Vol. 39, 1986, pp. 379–399. Zbl0602.35031MR829846
  13. [13] J. Nitsche, Über die isoliertien Singularitäten der Lösungen von Δu=eu, Math. Z. Bd., Vol. 69, 1957, pp. 316–324. Zbl0078.09201MR96883
  14. [14] R. Osserman, On the Inequality Δu ≥f(u), Pacific J. Math., Vol. 7, 1957, pp. 1641–1647. Zbl0083.09402MR98239
  15. [15] Y. Richard, Solutions Singulières d'Equations Elliptiques Semi-Linéaries, Ph. D. Thesis, Univ. Tours, 1987. 
  16. [16] Y. Richard and L. Veron, Un résultat d'isotropie pour des singularités d'inéquations elliptiques non linéaires, C.R. Acad. Sci. Paris, 304, série I, 1987, pp. 423–426. Zbl0634.35026MR888238
  17. [17] J. Serrin, Local Behaviour of Solutions of Quasilinear Equations, Acta Math., Vol 111, 1964, pp. 247–302. Zbl0128.09101MR170096
  18. [18] J. Serrin, Isolated Singularities of Solutions of Quasilinear Equations, Acta Math., Vol. 113, 1965, pp. 219-240. Zbl0173.39202MR176219
  19. [19] J.L. Vazquez, An a priori Interior Estimate for the Solutions of a Nonlinear Problem Representing Weak Diffusion, Nonlinear Anal., Vol. 5, 1981, pp. 95-103. Zbl0446.35018MR597285
  20. [20] J.L. Vazquez, On a Semilinear Equation in R2 Involving Bounded Measures, Proc. Roy. Soc. Edinburgh, Vol. 95A, 1983, pp. 181-202. Zbl0536.35025MR726870
  21. [21] J.L. Vazquez and L. Veron, Singularities of Elliptic Equations with an ExponentialNonlinearity, Math. Ann., Vol. 269, 1984, pp. 119-135. Zbl0567.35034MR756780
  22. [22] J.L. Vazquez and L. Veron, Isolated Singularities of Some Semilinear Elliptic Equations, J. Diff. Equ., Vol. 60, 1985, pp. 301-321. Zbl0549.35043MR811769
  23. [23] L. Veron, Singular Solutions of Some Nonlinear Elliptic Equations, Nonlinear Anal., Vol. 5, 1981, pp. 225-242. Zbl0457.35031MR607806
  24. [24] L. Veron, Weak and Strong Singularities of Nonlinear Elliptic Equations, Proc. Symp. Pure Math., Vol. 45, (2), 1986, pp. 477-495. Zbl0617.35044MR843634

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