Some remarks on a class of elliptic equations with degenerate coercivity

Lucio Boccardo; Haïm Brezis

Bollettino dell'Unione Matematica Italiana (2003)

  • Volume: 6-B, Issue: 3, page 521-530
  • ISSN: 0392-4041

Abstract

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We study degenerate elliptic problems of the type - div ∇ u ( 1 + | u | ) θ = f in Ω u = 0 on Ω .

How to cite

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Boccardo, Lucio, and Brezis, Haïm. "Some remarks on a class of elliptic equations with degenerate coercivity." Bollettino dell'Unione Matematica Italiana 6-B.3 (2003): 521-530. <http://eudml.org/doc/196016>.

@article{Boccardo2003,
abstract = {We study degenerate elliptic problems of the type \begin\{equation\} \{\left\lbrace \begin\{array\}\{ll\} - \text\{div\}\, \left( \frac\{\nabla u \}\{(1+|u|)^\{\theta \}\} \right) = f & \text\{in \} \Omega \\ u=0 & \text\{on \} \Omega . \end\{array\}\right.\} \end\{equation\}},
author = {Boccardo, Lucio, Brezis, Haïm},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {521-530},
publisher = {Unione Matematica Italiana},
title = {Some remarks on a class of elliptic equations with degenerate coercivity},
url = {http://eudml.org/doc/196016},
volume = {6-B},
year = {2003},
}

TY - JOUR
AU - Boccardo, Lucio
AU - Brezis, Haïm
TI - Some remarks on a class of elliptic equations with degenerate coercivity
JO - Bollettino dell'Unione Matematica Italiana
DA - 2003/10//
PB - Unione Matematica Italiana
VL - 6-B
IS - 3
SP - 521
EP - 530
AB - We study degenerate elliptic problems of the type \begin{equation} {\left\lbrace \begin{array}{ll} - \text{div}\, \left( \frac{\nabla u }{(1+|u|)^{\theta }} \right) = f & \text{in } \Omega \\ u=0 & \text{on } \Omega . \end{array}\right.} \end{equation}
LA - eng
UR - http://eudml.org/doc/196016
ER -

References

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  1. ALVINO, A.- FERONE, V.- TROMBETTI, G., A priori estimates for a class of non uniformly elliptic equations, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), suppl., 381-391. Zbl0911.35025MR1645729
  2. ALVINO, A.- BOCCARDO, L.- FERONE, V.- ORSINA, L.- TROMBETTI, G., Existence results for nonlinear elliptic equations with degenerate coercivity, preprint. Zbl1105.35040MR1970464
  3. BENILAN, P.- BOCCARDO, L.- GALLOUËT, T.- GARIEPY, R.- PIERRE, M.- VAZQUEZ, J.L., An L 1 theory of existence and uniqueness of nonlinear elliptic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 22 (1995), 240-273. Zbl0866.35037MR1354907
  4. BENILAN, P.- BREZIS, H.- CRANDALL, M. G., A semilinear equation in L 1 ⁢ R N , Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 2, no. 4 (1975), 523-555. Zbl0314.35077MR390473
  5. BOCCARDO, L.- DALL'AGLIO, A.- ORSINA, L.: Existence and regularity results for some elliptic equations with degenerate coercivity, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), suppl., 51-81. Zbl0911.35049MR1645710
  6. BOCCARDO, L.- GALLOUËT, T.: Nonlinear elliptic equations with right-hand side measures, Comm. Partial Differential Equations, 17 (1992), 641-655. Zbl0812.35043MR1163440
  7. BOCCARDO, L.- GIACHETTI, D., L s -regularity of solutions of some nonlinear elliptic problems, preprint. 
  8. BREZIS, H.- STRAUSS, W.A., Semi-linear second-order elliptic equations in L 1 , J. Math. Soc. Japan, 25 (1973), 565-590. Zbl0278.35041MR336050
  9. HARTMAN, P.- STAMPACCHIA, G.: On some nonlinear elliptic differential-functional equations, Acta Math., 115 (1966), 271-310. Zbl0142.38102MR206537
  10. PORRETTA, A., Uniqueness and homogenization for a class of non coercive operators in divergence form, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), suppl., 915-936. Zbl0914.35049MR1645762
  11. STAMPACCHIA, G., Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier (Grenoble), 15 (1965), 189-258. Zbl0151.15401MR192177

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