Boccardo, Lucio:
Positive solutions for some quasilinear elliptic equations with natural growths (Soluzioni positive per alcune equazioni ellittiche con crescite naturali)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni Serie 9 11 (2000), fasc. n.1, p. 31-39, (English)
pdf (361 Kb), djvu (125 Kb). | MR1797052 | Zbl 0970.35061
Sunto
È provato un teorema di esistenza di soluzioni per una classe di equazioni ellittiche quasi-lineari, con coefficienti a crescite naturali (come suggerito dal Calcolo delle variazioni). Il problema modello è il seguente
$$
\begin{cases}
- \text{div} ((1+ |u|^{r}) \nabla u) + |u|^{m-2} u |\nabla u|^{2} = f \quad &\text{in} \, \Omega \\
u = 0 &\text{su} \, \partial\Omega.
\end{cases}
$$
Referenze Bibliografiche
[1]
P. Benilan -
L. Boccardo -
T. Gallouët -
R. Gariepy -
M. Pierre -
J. L. Vazquez,
An $ L^{1} $-theory of existence and uniqueness of solutions of nonlinear elliptic equations.
Ann. Scuola Norm. Sup. Pisa Cl. Sci.,
22,
1995, 241-273. |
fulltext EuDML |
fulltext mini-dml |
MR 1354907 |
Zbl 0866.35037[3] L. Boccardo, Calcolo delle Variazioni. Roma 1 University PhD course, 1996.
[4]
L. Boccardo,
Some nonlinear Dirichlet problems in $ L^{1} $ involving lower order terms in divergence form. In:
A. Alvino et al. (eds),
Progress in elliptic and parabolic partial differential equations (Capri, 1994).
Pitman Res. Notes Math. Ser.,
350,
Longman, Harlow
1996, 43-57. |
MR 1430139 |
Zbl 0889.35034[5]
L. Boccardo -
T. Gallouët,
Strongly nonlinear elliptic equations having natural growth terms and $ L^{1} $ data.
Nonlinear Anal.,
19,
1992, 573-579. |
fulltext (doi) |
MR 1183664 |
Zbl 0795.35031[6]
L. Boccardo -
T. Gallouët -
L. Orsina,
Existence and nonexistence of solutions for some nonlinear elliptic equations.
J. Anal. Math.,
73,
1997, 203-223. |
fulltext (doi) |
MR 1616410 |
Zbl 0898.35035[8]
L. Boccardo -
F. Murat -
J.-P. Puel,
$ L^{\infty} $ estimate for some nonlinear elliptic partial differential equations and application to an existence result.
SIAM J. Math. Anal.,
23,
1992, 326-333. |
fulltext (doi) |
MR 1147866 |
Zbl 0785.35033[9]
H. Brezis -
F. E. Browder,
Some properties of higher order Sobolev spaces.
J. Math. Pures Appl.,
61,
1982, 245-259. |
MR 690395 |
Zbl 0512.46034[10]
H. Brezis -
L. Nirenberg,
Removable singularities for nonlinear elliptic equations.
Topol. Methods Nonlinear Anal.,
9,
1997, 201-219. |
MR 1491843 |
Zbl 0905.35027[11]
B. Dacorogna,
Direct methods in the calculus of variations.
Applied Mathematical Sciences,
78.
Springer-Verlag, Berlin-New York
1989. |
MR 990890 |
Zbl 0703.49001[12]
T. Del Vecchio,
Strongly nonlinear problems with Hamiltonian having natural growth.
Houston J. Math.,
16,
1990, 7-24. |
MR 1071263 |
Zbl 0714.35035[13]
J.-L. Lions,
Quelques méthodes de résolution des problèmes aux limites non linéaires.
Dunod, Paris
1969. |
Zbl 0189.40603[14]
A. Porretta,
Some remarks on the regularity of solutions for a class of elliptic equations with measure data. Preprint, Dip. Mat. Roma 1. |
MR 1814734 |
Zbl 0974.35032