Geodesic
Existence of a renormalized solution to a nonlinear elliptic equation with $L_1$-data in the space $\mathbb{R}^n$
Contemporary Mathematics. Fundamental Directions, Functional spaces. Differential operators. Problems of mathematics education, Tome 70 (2024) no. 2, pp. 278-299

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We consider a second-order quasilinear elliptic equation with an integrable right-hand side in the space $\mathbb{R}^n.$ Restrictions on the structure of the equation are formulated in terms of a generalized $N$-function. In the nonreflexive Muzilak–Orlicz–Sobolev spaces, the existence of a renormalized solution in the space $\mathbb{R}^n$ is proved.
Keywords: quasilinear equation, generalized $N$-function, Muzilak–Orlicz–Sobolev space, renormalized solution.
Mots-clés : elliptic equation 
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     author = {L. M. Kozhevnikova},
     title = {Existence of a renormalized solution to a nonlinear elliptic equation with $L_1$-data in the space $\mathbb{R}^n$},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {278--299},
     publisher = {mathdoc},
     volume = {70},
     number = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2024_70_2_a5/}
}
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L. M. Kozhevnikova. Existence of a renormalized solution to a nonlinear elliptic equation with $L_1$-data in the space $\mathbb{R}^n$. Contemporary Mathematics. Fundamental Directions, Functional spaces. Differential operators. Problems of mathematics education, Tome 70 (2024) no. 2, pp. 278-299. http://geodesic.mathdoc.fr/item/CMFD_2024_70_2_a5/