Статья
2020
Equivalence of Entropy and Renormalized Solutions of Anisotropic Elliptic Problem in Unbounded Domains with Measure Data
L. M. Kozhevnikova
Русская математика
https://doi.org/10.3103/S1066369X20010041
Abstract / Full Text
We consider a class of anisotropic elliptic equations of second order with variable exponents of non-linearity where a special Radon measure is used as the right-hand side. We establish uniqueness of entropy and renormalized solutions of the Dirichlet problem in anisotropic Sobolev spaces with variable exponents of non-linearity for arbitrary domains and certain other their properties. In addition, we prove the equivalence of entropy and renormalized solutions of the problem under consideration.
Author information
- Sterlitamak Branch of Bashkir State University, 31 Lenin Ave., Sterlitamak, 453103, RussiaL. M. Kozhevnikova
- Elabuga Branch of Kazan Federal University, 89 Kazanskaya str., Elabuga, 423600, RussiaL. M. Kozhevnikova
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