Geodesic
Existence of Renormalized Solutions for Some Anisotropic Quasilinear Elliptic Equations
Kragujevac Journal of Mathematics, Tome 44 (2020) no. 4, p. 617

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In this paper, we consider a class of anisotropic quasilinear elliptic equations of the type $eft\{\begin{array}{ll} \displaystyle- um_{i=1}^{N} tial^{i}a_{i}(x,u,abla u) + |u|^{s(x)-1}u = f(x,u), \mbox{in } mega, u = 0 ext{on } tialmega, \end{array} \right.$ where $f(x,s)$ is a Carathéodory function which satisfies some growth condition. We prove the existence of renormalized solutions for our Dirichlet problem, and some regularity results are concluded.
Classification : 35J62 35J20
Keywords: anisotropic Sobolev spaces, variable exponents, quasilinear elliptic equations, renormalized solutions 
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     author = {T. Ahmedatt and A. Ahmed and H. Hjiaj and A. Touzani},
     title = {Existence of {Renormalized} {Solutions} for {Some} {Anisotropic} {Quasilinear} {Elliptic} {Equations}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {617 },
     publisher = {mathdoc},
     volume = {44},
     number = {4},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2020_44_4_a11/}
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T. Ahmedatt; A. Ahmed; H. Hjiaj; A. Touzani. Existence of Renormalized Solutions for Some Anisotropic Quasilinear Elliptic Equations. Kragujevac Journal of Mathematics, Tome 44 (2020) no. 4, p. 617 . http://geodesic.mathdoc.fr/item/KJM_2020_44_4_a11/