Equivalence of Entropy and Renormalized Solutions of a Nonlinear Elliptic Problem in Musielak–Orlicz Spaces

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We consider second-order elliptic equations with nonlinearities determined by Musielak–Orlicz functions and with right-hand side in the space. In the Musielak–Orlicz–Sobolev spaces, we establish some properties and uniqueness of both entropy and renormalized solutions of the Dirichlet problem in domains with Lipschitz boundary. In addition, the equivalence and sign-definiteness of the entropy and renormalized solutions is proved.

作者简介

L. Kozhevnikova

Sterlitamak Branch of Bashkir University of Science and Technology, Sterlitamak, Bashkortostan, 453103, Russia; Elabuga Institute of Kazan Federal University, Elabuga, Tatarstan, 423600, Russia

Email: kosul@mail.ru
г. Стерлитамак, Россия;г. Елабуга, Россия

A. Kashnikova

Sterlitamak Branch of Bashkir University of Science and Technology, Sterlitamak, Bashkortostan, 453103, Russia

编辑信件的主要联系方式.
Email: a.kashnikova98@yandex.ru
г. Стерлитамак, Россия

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