Bounded Solutions for Some Dirichlet Problems with L^{1}(\Omega) Data

Tommaso Leonori

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 3, page 785-795
  • ISSN: 0392-4041

Abstract

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In this paper we prove the existence of a solution for a problem whose model is: \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} with f(x) in L^{1}(\Omega) and \sigma, \gamma>0.

How to cite

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Leonori, Tommaso. "Bounded Solutions for Some Dirichlet Problems with $L^1(\Omega)$ Data." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 785-795. <http://eudml.org/doc/290364>.

@article{Leonori2007,
abstract = {In this paper we prove the existence of a solution for a problem whose model is: \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*\} with $f(x)$ in $L^\{1\}(\Omega)$ and $\sigma$, $\gamma > 0$.},
author = {Leonori, Tommaso},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {785-795},
publisher = {Unione Matematica Italiana},
title = {Bounded Solutions for Some Dirichlet Problems with $L^1(\Omega)$ Data},
url = {http://eudml.org/doc/290364},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Leonori, Tommaso
TI - Bounded Solutions for Some Dirichlet Problems with $L^1(\Omega)$ Data
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 785
EP - 795
AB - In this paper we prove the existence of a solution for a problem whose model is: \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*} with $f(x)$ in $L^{1}(\Omega)$ and $\sigma$, $\gamma > 0$.
LA - eng
UR - http://eudml.org/doc/290364
ER -

References

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  7. BREZIS, H. - STRAUSS, W. A., Semi-linear second-order elliptic equations in L^{1}, J. Math. Soc. Japan, 25 (1973), 565-590. Zbl0278.35041MR336050DOI10.2969/jmsj/02540565
  8. DUPAIGNE, L. - PONCE, A. C. - PORRETTA, A., Elliptic equations with vertical asymptotes in the nonlinear term, J. Anal. Math., 98 (2006), 349-396. Zbl1132.35366MR2254490DOI10.1007/BF02790280
  9. LERAY, J. - LIONS, J. L., Quelque resultat de Višik sur les problémes elliptiques non linéaires par les méthodes de Minty-Browder, Bull. Soc. Math. France, 93 (1965), 97-107. Zbl0132.10502MR194733

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