Breaking of resonance and regularizing effect of a first order quasi-linear term in some elliptic equations

Boumediene Abdellaoui; Ireneo Peral; Ana Primo

Annales de l'I.H.P. Analyse non linéaire (2008)

  • Volume: 25, Issue: 5, page 969-985
  • ISSN: 0294-1449

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Abdellaoui, Boumediene, Peral, Ireneo, and Primo, Ana. "Breaking of resonance and regularizing effect of a first order quasi-linear term in some elliptic equations." Annales de l'I.H.P. Analyse non linéaire 25.5 (2008): 969-985. <http://eudml.org/doc/78821>.

@article{Abdellaoui2008,
author = {Abdellaoui, Boumediene, Peral, Ireneo, Primo, Ana},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {quasilinear elliptic equations; existence and nonexistence; regularization; resonance},
language = {eng},
number = {5},
pages = {969-985},
publisher = {Elsevier},
title = {Breaking of resonance and regularizing effect of a first order quasi-linear term in some elliptic equations},
url = {http://eudml.org/doc/78821},
volume = {25},
year = {2008},
}

TY - JOUR
AU - Abdellaoui, Boumediene
AU - Peral, Ireneo
AU - Primo, Ana
TI - Breaking of resonance and regularizing effect of a first order quasi-linear term in some elliptic equations
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2008
PB - Elsevier
VL - 25
IS - 5
SP - 969
EP - 985
LA - eng
KW - quasilinear elliptic equations; existence and nonexistence; regularization; resonance
UR - http://eudml.org/doc/78821
ER -

References

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  1. [1] Abdellaoui B., Dall'Aglio A., Peral I., Some remarks on elliptic problems with critical growth on the gradient, J. Differential Equations222 (1) (2006) 21-62. Zbl05013584MR2200746
  2. [2] Abdellaoui B., Peral I., The equation - Δ u - λ u x 2 = u p + c f x : The optimal power, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)VI (2007) 1-25. Zbl1181.35080MR2341519
  3. [3] Abdellaoui B., Peral I., Primo A., Some elliptic problems with Hardy potential and critical growth in the gradient: non-resonance and blow-up results, J. Differential Equations239 (2007) 386-416. Zbl1331.35128MR2344278
  4. [4] Alaa N., Pierre M., Weak solutions of some quasilinear elliptic equations with data measures, SIAM. J. Math. Anal.24 (1) (1993) 23-35. Zbl0809.35021MR1199524
  5. [5] Boccardo L., Gallouët T., Orsina L., Existence and nonexistence of solutions for some nonlinear elliptic equations, J. Anal. Math.73 (1997) 203-223. Zbl0898.35035MR1616410
  6. [6] Boccardo L., Murat F., Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations, Nonlinear Anal. TMA19 (6) (1992) 581-597. Zbl0783.35020MR1183665
  7. [7] Boccardo L., Murat F., Puel J.P., Existence de solutions faibles pour des équations elliptiques quasi-linéaires à croissance quadratique, in: Lions L., Brezis H. (Eds.), Nonlinear Partial Differential Equations and their Applications, Collège de France Seminar, vol. IV, Research Notes in Math, vol. 84, Pitman, London, 1983, pp. 19-73. Zbl0588.35041MR716511
  8. [8] Boccardo L., Murat F., Puel J.P., Resultats d'existence pour certains problèmes elliptiques quasi-linéaires, Ann. Sc. Norm. Sup. Pisa11 (2) (1984) 213-235. Zbl0557.35051MR764943
  9. [9] Boccardo L., Murat F., Puel J.P., Existence des solutions non bornées pour certains équations quasi-linéaires, Portugal. Math.41 (1982) 507-534. Zbl0524.35041MR766873
  10. [10] Boccardo L., Orsina L., Peral I., A remark on existence and optimal summability of solutions of elliptic problems involving Hardy potential, Discrete and Continuous Dynamical Systems16 (3) (2006) 513-523. Zbl05141172MR2257147
  11. [11] Brezis H., Kamin S., Sublinear elliptic equations in R N , Manuscripta Math.74 (1992) 87-106. Zbl0761.35027MR1141779
  12. [12] Brezis H., Lieb E.H., A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer. Math. Soc.88 (1983) 486-490. Zbl0526.46037MR699419
  13. [13] Brezis H., Ponce A., Kato's inequality when Δu is a measure, C. R. Acad. Sci. Paris, Ser. I338 (2004) 599-604. Zbl1101.35028MR2056467
  14. [14] Brezis H., Strauss W.A., Semilinear second order elliptic equations in L 1 , J. Math. Soc. Japan25 (1973) 565-590. Zbl0278.35041MR336050
  15. [15] Dal Maso G., Murat F., Orsina L., Prignet A., Renormalized solutions of elliptic equations with general measure data, Ann. Sc. Norm. Super. Pisa Cl. Sci.28 (4) (1999) 741-808. Zbl0958.35045MR1760541
  16. [16] Bénilan P., Boccardo L., Gallouët T., Gariepy R., Pierre M., Vazquez J.L., An L 1 -theory of existence and uniqueness of solutions of nonlinear elliptic equations, Ann. Sc. Norm. Super. Pisa Cl. Sci.22 (2) (1995) 241-273. Zbl0866.35037MR1354907
  17. [17] Ferone V., Murat V.F., Quasilinear problems having quadratic growth in the gradient: an existence result when the source term is small, in: Equations aux dérivées partialles et applications, Gauthier-Villars, Ed. Sci. Méd. Elsevier, Paris, 1998, pp. 497-515. Zbl0917.35039MR1648236
  18. [18] Garcia Azorero J., Peral I., Hardy inequalities and some critical elliptic and parabolic problems, J. Differential Equations144 (1998) 441-476. Zbl0918.35052MR1616905
  19. [19] Hansson K., Maz'ya V.G., Verbitsky I.E., Criteria of solvability for multidimensional Riccati equations, Ark. Mat.37 (1999) 87-120. Zbl1087.35513MR1673427
  20. [20] Kato T., Schrödinger operators with singular potentials, Israel J. Math.13 (1972) 135-148. Zbl0246.35025MR333833
  21. [21] Lieb E.H., Loos M., Analysis, Graduate Studies in Mathematics, vol. 14, American Mathematical Society, Providence, RI, 2001. Zbl0966.26002MR1817225
  22. [22] Lions P.L., Résolution de problèmes elliptiques quasilinéaires, Arch. Rational Mech. Anal.74 (4) (1980) 335-353. Zbl0449.35036MR588033
  23. [23] Pucci P., Serrin J., The strong maximum principle revisited, J. Differential Equations196 (1) (2004) 1-66. Zbl1109.35022MR2025185
  24. [24] Stampacchia G., Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier15 (1965) 189-258. Zbl0151.15401MR192177

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