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Sobolev–Dirichlet problem for quasilinear elliptic equations in generalized Orlicz–Sobolev spaces

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Abstract

In this paper, we prove existence, uniqueness, and local regularity of the solution to the Sobolev–Dirichlet problem for quasilinear elliptic equations in the generalized Orlicz–Sobolev spaces on domains, not necessarily bounded, of \({\mathbb {R}}^N\). Our approach is based on solving the obstacle problem and using the Harnack inequality.

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Acknowledgements

We would like to thank the referees for their comments and remarks.

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  1. Department of Mathematics, Ibn Tofail University, BP 133, Kenitra, Morocco

    Allami Benyaiche & Ismail Khlifi

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  1. Allami Benyaiche
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  2. Ismail Khlifi
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Correspondence to Allami Benyaiche.

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Benyaiche, A., Khlifi, I. Sobolev–Dirichlet problem for quasilinear elliptic equations in generalized Orlicz–Sobolev spaces. Positivity 25, 819–841 (2021). https://doi.org/10.1007/s11117-020-00789-z

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  • DOI: https://doi.org/10.1007/s11117-020-00789-z

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