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Existence of an entropic solution of a nonlinear elliptic problem in an unbounded domain

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Abstract

We consider a second-order quasilinear elliptic equation with an integrable right-hand side. We formulate constraints on the structure of the equation in terms of a generalized \(N\)-function. We prove the existence of an entropic solution of the Dirichlet problem in nonreflexive Musielak–Orlicz–Sobolev spaces in an arbitrary unbounded strictly Lipschitz domain.

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Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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Authors and Affiliations

  1. Sterlitamak Branch, Ufa University of Science and Technology, Sterlitamak, Russia

    L. M. Kozhevnikova

  2. Elabuga Branch, Kazan (Volga Region) Federal University, Elabuga, Russia

    L. M. Kozhevnikova

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  1. L. M. Kozhevnikova
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Correspondence to L. M. Kozhevnikova.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2024, Vol. 218, pp. 124–148 https://doi.org/10.4213/tmf10535.

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Kozhevnikova, L.M. Existence of an entropic solution of a nonlinear elliptic problem in an unbounded domain. Theor Math Phys 218, 106–128 (2024). https://doi.org/10.1134/S0040577924010082

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