Geodesic
Some remarks on a class of elliptic equations with degenerate coercivity
Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 3, pp. 521-530.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We study degenerate elliptic problems of the type \begin{equation} \begin{cases} - \text{div}\, \left( \frac{\nabla u }{(1+|u|)^{\theta}} \right) = f \text{in } \Omega \\ u=0 \text{on } \Omega. \end{cases} \end{equation}
Si studiano problemi ellittici degeneri del tipo \begin{equation} \begin{cases} - \text{div}\, \left( \frac{\nabla u }{(1+|u|)^{\theta}} \right) = f \text{in } \Omega \\ u=0 \text{on } \Omega. \end{cases} \end{equation} 
@article{BUMI_2003_8_6B_3_a0,
     author = {Boccardo, Lucio and Brezis, Ha{\"\i}m},
     title = {Some remarks on a class of elliptic equations with degenerate coercivity},
     journal = {Bollettino della Unione matematica italiana},
     pages = {521--530},
     publisher = {mathdoc},
     volume = {Ser. 8, 6B},
     number = {3},
     year = {2003},
     zbl = {1178.35183},
     mrnumber = {1645729},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2003_8_6B_3_a0/}
}
TY  - JOUR
AU  - Boccardo, Lucio
AU  - Brezis, Haïm
TI  - Some remarks on a class of elliptic equations with degenerate coercivity
JO  - Bollettino della Unione matematica italiana
PY  - 2003
SP  - 521
EP  - 530
VL  - 6B
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BUMI_2003_8_6B_3_a0/
LA  - en
ID  - BUMI_2003_8_6B_3_a0
ER  - 
%0 Journal Article
%A Boccardo, Lucio
%A Brezis, Haïm
%T Some remarks on a class of elliptic equations with degenerate coercivity
%J Bollettino della Unione matematica italiana
%D 2003
%P 521-530
%V 6B
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BUMI_2003_8_6B_3_a0/
%G en
%F BUMI_2003_8_6B_3_a0
Boccardo, Lucio; Brezis, Haïm. Some remarks on a class of elliptic equations with degenerate coercivity. Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 3, pp. 521-530. http://geodesic.mathdoc.fr/item/BUMI_2003_8_6B_3_a0/

[1] A. Alvino-V. Ferone-G. Trombetti, A priori estimates for a class of non uniformly elliptic equations, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), suppl., 381-391. | MR | Zbl

[2] A. Alvino-L. Boccardo-V. Ferone-L. Orsina-G. Trombetti, Existence results for nonlinear elliptic equations with degenerate coercivity, preprint. | MR | Zbl

[3] P. Benilan-L. Boccardo-T. Gallouët-R. Gariepy-M. Pierre-J.L. Vazquez, An $L^1$ theory of existence and uniqueness of nonlinear elliptic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 22 (1995), 240-273. | fulltext mini-dml | MR | Zbl

[4] P. Benilan-H. Brezis-M. G. Crandall, A semilinear equation in $L^1(\mathbb{R}^N)$, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 2, no. 4 (1975), 523-555. | fulltext mini-dml | MR | Zbl

[5] L. Boccardo-A. Dall'Aglio-L. Orsina: Existence and regularity results for some elliptic equations with degenerate coercivity, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), suppl., 51-81. | MR | Zbl

[6] L. Boccardo-T. Gallouët: Nonlinear elliptic equations with right-hand side measures, Comm. Partial Differential Equations, 17 (1992), 641-655. | MR | Zbl

[7] L. Boccardo-D. Giachetti, $L^s$-regularity of solutions of some nonlinear elliptic problems, preprint.

[8] H. Brezis-W.A. Strauss, Semi-linear second-order elliptic equations in $L^1$, J. Math. Soc. Japan, 25 (1973), 565-590. | fulltext mini-dml | MR | Zbl

[9] P. Hartman-G. Stampacchia: On some nonlinear elliptic differential-functional equations, Acta Math., 115 (1966), 271-310. | MR | Zbl

[10] A. Porretta, Uniqueness and homogenization for a class of non coercive operators in divergence form, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), suppl., 915-936. | MR | Zbl

[11] G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier (Grenoble), 15 (1965), 189-258. | fulltext mini-dml | MR | Zbl