Local renormalized solutions of elliptic equations with variable exponents in unbounded domains
- Authors: Kozhevnikova L.M.1,2
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Affiliations:
- Ufa University of Science and Technology
- Elabuga Institute of Kazan Federal University
- Issue: Vol 71, No 1 (2025): Nonlocal and nonlinear problems
- Pages: 125-146
- Section: Articles
- URL: https://journals.rudn.ru/CMFD/article/view/43911
- DOI: https://doi.org/10.22363/2413-3639-2025-71-1-125-146
- EDN: https://elibrary.ru/UQKNFN
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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.
About the authors
L. M. Kozhevnikova
Ufa University of Science and Technology; Elabuga Institute of Kazan Federal University
Author for correspondence.
Email: kosul@mail.ru
Sterlitamak, Russia; Elabuga, Russia
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