@article{AIHPC_2008__25_5_969_0, author = {Abdellaoui, Boumediene and Peral, Ireneo and Primo, Ana}, title = {Breaking of resonance and regularizing effect of a first order quasi-linear term in some elliptic equations}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {969--985}, publisher = {Elsevier}, volume = {25}, number = {5}, year = {2008}, doi = {10.1016/j.anihpc.2007.06.003}, mrnumber = {2457819}, zbl = {1156.35036}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2007.06.003/} }
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 SP - 969 EP - 985 VL - 25 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2007.06.003/ DO - 10.1016/j.anihpc.2007.06.003 LA - en ID - AIHPC_2008__25_5_969_0 ER -
%0 Journal Article %A Abdellaoui, Boumediene %A Peral, Ireneo %A Primo, Ana %T Breaking of resonance and regularizing effect of a first order quasi-linear term in some elliptic equations %J Annales de l'I.H.P. Analyse non linéaire %D 2008 %P 969-985 %V 25 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2007.06.003/ %R 10.1016/j.anihpc.2007.06.003 %G en %F AIHPC_2008__25_5_969_0
Abdellaoui, Boumediene; Peral, Ireneo; 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, Tome 25 (2008) no. 5, pp. 969-985. doi : 10.1016/j.anihpc.2007.06.003. http://www.numdam.org/articles/10.1016/j.anihpc.2007.06.003/
[1] Some remarks on elliptic problems with critical growth on the gradient, J. Differential Equations 222 (1) (2006) 21-62. | MR
, , ,[2] The equation : The optimal power, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) VI (2007) 1-25. | Numdam | MR
, ,[3] Some elliptic problems with Hardy potential and critical growth in the gradient: non-resonance and blow-up results, J. Differential Equations 239 (2007) 386-416. | MR
, , ,[4] Weak solutions of some quasilinear elliptic equations with data measures, SIAM. J. Math. Anal. 24 (1) (1993) 23-35. | MR | Zbl
, ,[5] Existence and nonexistence of solutions for some nonlinear elliptic equations, J. Anal. Math. 73 (1997) 203-223. | MR | Zbl
, , ,[6] Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations, Nonlinear Anal. TMA 19 (6) (1992) 581-597. | MR | Zbl
, ,[7] Existence de solutions faibles pour des équations elliptiques quasi-linéaires à croissance quadratique, in: , (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. | MR | Zbl
, , ,[8] Resultats d'existence pour certains problèmes elliptiques quasi-linéaires, Ann. Sc. Norm. Sup. Pisa 11 (2) (1984) 213-235. | Numdam | MR | Zbl
, , ,[9] Existence des solutions non bornées pour certains équations quasi-linéaires, Portugal. Math. 41 (1982) 507-534. | MR | Zbl
, , ,[10] A remark on existence and optimal summability of solutions of elliptic problems involving Hardy potential, Discrete and Continuous Dynamical Systems 16 (3) (2006) 513-523. | MR
, , ,[11] Sublinear elliptic equations in , Manuscripta Math. 74 (1992) 87-106. | MR | Zbl
, ,[12] A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer. Math. Soc. 88 (1983) 486-490. | MR | Zbl
, ,[13] Kato's inequality when Δu is a measure, C. R. Acad. Sci. Paris, Ser. I 338 (2004) 599-604. | MR | Zbl
, ,[14] Semilinear second order elliptic equations in , J. Math. Soc. Japan 25 (1973) 565-590. | MR | Zbl
, ,[15] Renormalized solutions of elliptic equations with general measure data, Ann. Sc. Norm. Super. Pisa Cl. Sci. 28 (4) (1999) 741-808. | Numdam | MR | Zbl
, , , ,[16] An -theory of existence and uniqueness of solutions of nonlinear elliptic equations, Ann. Sc. Norm. Super. Pisa Cl. Sci. 22 (2) (1995) 241-273. | Numdam | MR | Zbl
, , , , , ,[17] 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. | MR | Zbl
, ,[18] Hardy inequalities and some critical elliptic and parabolic problems, J. Differential Equations 144 (1998) 441-476. | MR | Zbl
, ,[19] Criteria of solvability for multidimensional Riccati equations, Ark. Mat. 37 (1999) 87-120. | MR | Zbl
, , ,[20] Schrödinger operators with singular potentials, Israel J. Math. 13 (1972) 135-148. | MR | Zbl
,[21] Analysis, Graduate Studies in Mathematics, vol. 14, American Mathematical Society, Providence, RI, 2001. | MR | Zbl
, ,[22] Résolution de problèmes elliptiques quasilinéaires, Arch. Rational Mech. Anal. 74 (4) (1980) 335-353. | MR | Zbl
,[23] The strong maximum principle revisited, J. Differential Equations 196 (1) (2004) 1-66. | MR | Zbl
, ,[24] Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier 15 (1965) 189-258. | Numdam | MR | Zbl
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