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On Solutions of Nonlinear Elliptic Equations with \(\boldsymbol{L}_{\mathbf{1}}\)-Data in Unbounded Domains

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Abstract

In this work, we consider second-order elliptic equations with nonlinearities determined by Musielak–Orlicz functions and summable right-hand side. The equivalence of entropy solutions and renormalized solutions of the Dirichlet problem in arbitrary unbounded domains with Lipschitz boundary is established. The existence and uniqueness of both entropy solutions and renormalized solutions are proved in nonreflexive Musielak–Orlicz–Sobolev spaces.

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Correspondence to L. M. Kozhevnikova.

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(Submitted by A. B. Muravnik)

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Kozhevnikova, L.M. On Solutions of Nonlinear Elliptic Equations with \(\boldsymbol{L}_{\mathbf{1}}\)-Data in Unbounded Domains. Lobachevskii J Math 44, 1879–1901 (2023). https://doi.org/10.1134/S1995080223050372

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  • DOI: https://doi.org/10.1134/S1995080223050372

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