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Contemporary Mathematics. Fundamental Directions, 2024, Volume 70, Issue 2, Pages 278–299
DOI: https://doi.org/10.22363/2413-3639-2024-70-2-278-299
(Mi cmfd541)
 

Existence of a renormalized solution to a nonlinear elliptic equation with $L_1$-data in the space $\mathbb{R}^n$

L. M. Kozhevnikovaab

a Ufa University of Science and Technology, Ufa, Russia
b Elabuga Institute of Kazan Federal University, Elabuga, Russia
References:
Abstract: 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, elliptic equation, generalized $N$-function, Muzilak–Orlicz–Sobolev space, renormalized solution.
Bibliographic databases:
Document Type: Article
UDC: 517.956.25
Language: Russian
Citation: L. M. Kozhevnikova, “Existence of a renormalized solution to a nonlinear elliptic equation with $L_1$-data in the space $\mathbb{R}^n$”, Functional spaces. Differential operators. Problems of mathematics education, CMFD, 70, no. 2, Российский университет дружбы народов, M., 2024, 278–299
Citation in format AMSBIB
\Bibitem{Koz24}
\by L.~M.~Kozhevnikova
\paper Existence of a renormalized solution to a nonlinear elliptic equation with $L_1$-data in the space $\mathbb{R}^n$
\inbook Functional spaces. Differential operators. Problems of mathematics education
\serial CMFD
\yr 2024
\vol 70
\issue 2
\pages 278--299
\publ Российский университет дружбы народов
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd541}
\crossref{https://doi.org/10.22363/2413-3639-2024-70-2-278-299}
\edn{https://elibrary.ru/YKDZHU}
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