Existence of entropy solutions for nonlinear elliptic equations in Musielak framework with L1 data
| Autor: | Elemine Vall Mohamed Saad Bouh, A. Ahmed, A. Touzani, A. Benkirane |
|---|---|
| Jazyk: | English<br />Portuguese |
| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Boletim da Sociedade Paranaense de Matemática, Vol 36, Iss 1, Pp 125-150 (2018) |
| Druh dokumentu: | article |
| ISSN: | 0037-8712 2175-1188 |
| DOI: | 10.5269/bspm.v36i1.29440 |
| Popis: | We prove existence of solutions for strongly nonlinear elliptic equations of the form $$ \left\{\begin{array}{c} A(u)+g(x,u,\nabla u)=f+\mbox {div}(\phi(u))\quad \textrm{in }\Omega, \\ u\equiv0\quad \partial \Omega. \end{array} \right.$$ Where $A(u)=-\mbox {div}(a(x,u,\nabla u))$ be a Leray-Lions operator defined in $D(A)\subset W^{1}_{0}L_\varphi(\Omega) \rightarrow W^{-1}_{0}L_\psi(\Omega)$, the right hand side belongs in $ L^{1}(\Omega)$, and $\phi\in C^{0}(\mathbb{R},\mathbb{R}^N)$, without assuming the $\Delta_{2}$-condition on the Musielak function. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|