Leonori, Tommaso:
Bounded Solutions for Some Dirichlet Problems with $L^1(\Omega)$ Data
Bollettino dell'Unione Matematica Italiana Serie 8 10-B (2007), fasc. n.3, p. 785-795, Unione Matematica Italiana (English)
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Sunto
In questo lavoro viene dimostrata l'esistenza di una soluzione per un problema il cui modello è: \begin{equation*} \begin{cases} -\Delta u + \frac{u}{\sigma - |u|} = \gamma |\nabla u|^{2} + f(x) & \text{in } \Omega \\ u = 0 & \text{on } \partial \Omega \end{cases} \end{equation*} con $f(x)$ in $L^{1}(\Omega)$ e $\sigma$, $\gamma > 0$.
Referenze Bibliografiche
[1]
P. BÉNILAN -
L. BOCCARDO.
T. GALLOUËTT -
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 |
MR 1354907[2]
P. BÉNILAN -
H. BREZIS -
M. C. CRANDALL,
A semilinear equation in $L^1(\mathbb{R}^N)$,
Ann. Scuola Norm. Sup. Pisa Cl. Sci.,
2, no. 4 (
1975), 523-555. |
fulltext EuDML |
MR 390473[4]
L. BOCCARDO -
T. GALLOUËT,
Nonlinear elliptic and parabolic equations involving measure data,
J. Funct. Anal.,
87 (
1989), 149-169. |
fulltext (doi) |
MR 1025884[5]
L. BOCCARDO -
F. MURAT -
J. P. PUEL,
Existence of bounded solutions for nonlinear elliptic unilateral problems,
Ann. Mat. Pura Appl.,
152 (
1988), 183-196. |
fulltext (doi) |
MR 980979 |
Zbl 0687.35042[6]
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, no. 2 (
1992), 326-333. |
fulltext (doi) |
MR 1147866 |
Zbl 0785.35033[8]
L. DUPAIGNE -
A. C. PONCE -
A. PORRETTA,
Elliptic equations with vertical asymptotes in the nonlinear term,
J. Anal. Math.,
98 (
2006), 349-396. |
fulltext (doi) |
MR 2254490 |
Zbl 1132.35366[9]
J. LERAY -
J. L. LIONS,
Quelque resultat de Višik sur les problémes elliptiques non linéaires par les méthodes de Minty-Browder,
Bull. Soc. Math. France,
93 (
1965), 97-107. |
fulltext EuDML |
MR 194733 |
Zbl 0132.10502