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Contemporary Mathematics. Fundamental Directions, 2025, Volume 71, Issue 1, Pages 125–146
DOI: https://doi.org/10.22363/2413-3639-2025-71-1-125-146 (Mi cmfd578) 		 
Local renormalized solutions of elliptic equations with variable exponents in unbounded domains

L. M. Kozhevnikovaab

a Sterlitamak Branch of Ufa University of Science and Technology, Sterlitamak, Russia
b Elabuga Institute of Kazan Federal University, Elabuga, Russia
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DOI: https://doi.org/10.22363/2413-3639-2025-71-1-125-146
Abstract: In this paper, we consider a second-order quasilinear elliptic equation with variable nonlinearity exponents and a locally summable right-hand side. The stability property is established and, as a consequence, the existence of a local renormalized solution of the Dirichlet problem in an arbitrary unbounded domain is proved.
Keywords: quasilinear elliptic equation, variable growth exponent, unbounded domain, Dirichlet problem, stability of solution, local renormalized solution.
Bibliographic databases:
Document Type: Article
UDC: 517.956.25
Language: Russian
Citation: L. M. Kozhevnikova, “Local renormalized solutions of elliptic equations with variable exponents in unbounded domains”, Nonlocal and nonlinear problems, CMFD, 71, no. 1, PFUR, M., 2025, 125–146
Citation in format AMSBIB
\Bibitem{Koz25}
\by L.~M.~Kozhevnikova
\paper Local renormalized solutions of elliptic equations with variable exponents in~unbounded domains
\inbook Nonlocal and nonlinear problems
\serial CMFD
\yr 2025
\vol 71
\issue 1
\pages 125--146
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd578}
\edn{https://elibrary.ru/UQKNFN}
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