Research Communication | Open Access
Volume 2021 | Communication ID 174
Volume 2021 | Communication ID 174
| Strongly nonlinear degenerated elliptic equations with weight and $\emph{ L}^1$ data |
Mohamed El Ouaarabi, Chakir Allalou, Adil Abbassi
Received |
Accepted |
Published |
January 30, 2021 |
February 15, 2021 |
March 15, 2021 |
Abstract: In this paper, we prove the existence and uniqueness of solution for the Dirichlet problem associated to the strongly nonlinear degenerate elliptic equation of the type: \begin{equation*} \begin{cases} -{\rm{div}}\Big[ \omega_{1}\mathcal{A}(x,\nabla u)+\omega_{2}\mathcal{B}(x,u,\nabla u)\Big]+\omega_{3}g(x)u(x)=f \quad \hspace{+1cm}\mbox{in}\;\Omega,\\ \;u(x)=0 \;\;\qquad\qquad \hspace{+6cm} \quad\quad \mbox{on} \;\partial\Omega, \end{cases} \end{equation*} in the setting of the weighted Sobolev spaces $W^{1,p}(\Omega,\omega_{1})$, where $\Omega$ is a bounded open set of ...