Convergence and partial regularity for weak solutions of some nonlinear elliptic equation : the supercritical case

Frank Pacard

Annales de l'I.H.P. Analyse non linéaire (1994)

  • Volume: 11, Issue: 5, page 537-551
  • ISSN: 0294-1449

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Pacard, Frank. "Convergence and partial regularity for weak solutions of some nonlinear elliptic equation : the supercritical case." Annales de l'I.H.P. Analyse non linéaire 11.5 (1994): 537-551. <http://eudml.org/doc/78343>.

@article{Pacard1994,
author = {Pacard, Frank},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {supercritical nonlinearity; Hausdorff dimension of the singular set},
language = {eng},
number = {5},
pages = {537-551},
publisher = {Gauthier-Villars},
title = {Convergence and partial regularity for weak solutions of some nonlinear elliptic equation : the supercritical case},
url = {http://eudml.org/doc/78343},
volume = {11},
year = {1994},
}

TY - JOUR
AU - Pacard, Frank
TI - Convergence and partial regularity for weak solutions of some nonlinear elliptic equation : the supercritical case
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1994
PB - Gauthier-Villars
VL - 11
IS - 5
SP - 537
EP - 551
LA - eng
KW - supercritical nonlinearity; Hausdorff dimension of the singular set
UR - http://eudml.org/doc/78343
ER -

References

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  1. [1] F. Bethuel, Partial Regularity for Stationary Harmonic Maps , to appear inManuscripta Math. Zbl0792.53039
  2. [2] S. Campanato, Proprieta di Inclusione per Spazi di Morrey, Ricerche Mat., Vol. 12, 1963, p. 67-86. Zbl0192.22703MR156228
  3. [3] S. Campanato, Equazioni Ellittiche del II Ordine e Spazi L(2,λ), Ann. Mat. Pura Appl., Vol. 4, 69, 1965, p. 321-381. Zbl0145.36603MR192168
  4. [4] L.C. Evans, Partial Regularity for Stationary Harmonic Maps into Spheres, Arch. Rational Mech. Anal., Vol. 116, 1991, p. 101-113. Zbl0754.58007MR1143435
  5. [5] M. Giaquinta, Multiple Integrals in the Calculus of Variations and Nonlinear Analysis, Annals of Mathematical Studies, Vol. 105, Princeton Univ. Press, 1989. Zbl0516.49003
  6. [6] D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of the Second Order, Springer, Berlin-Heidelberg-New York, 1977. Zbl0361.35003MR473443
  7. [7] R. Hardt, D. Kinderlehrer, F.H. Lin, Existence and Partial Regularity of Static Liquid Cristal Configurations, Comm. Math. Phys., Vol. 105, 1986, p. 547-570. Zbl0611.35077MR852090
  8. [8] C.B.Jr. Morrey, Multiple Integrals in the Calculus of Variations, Berlin-Heidelberg-New York, Springer, 1966. Zbl0142.38701MR202511
  9. [9] F. Pacard, A Note on the Regularity of Weak Solutions of -Δu = uα in Rn, n ≥ 3, Houston Journal of Math., Vol. 18, 4, 1982, p. 621-632. Zbl0819.35045MR1201489
  10. [10] F. Pacard, Partial Regularity for Weak Solutions of a Nonlinear Elliptic Equation , to appear inManuscripta Mathematica. Zbl0811.35011MR1216772
  11. [11] S.I. Pohozaev, Eigenfunctions of the Equation Δu + λf(u) = 0, Soviet. Math. Doklady, Vol. 6, 1965, p. 1408-1411. Zbl0141.30202MR192184
  12. [12] R. Schoen, Analytic Aspects for the Harmonic Map Problem, Math. Sci. Res. Inst. Publi., Vol. 2, Springer, Berlin, 1984. Zbl0551.58011MR765241

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