Abstract
We consider the Dirichlet problem in an arbitrary unbounded domain with inhomogeneous boundary conditions for a certain class of anisotropic elliptic equations whose right-hand sides belong to the class L1 and prove the existence of entropic solutions in anisotropic Sobolev–Orlicz spaces.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 139, Differential Equations. Mathematical Physics, 2017.
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Kozhevnikova, L.M. Existence of Entropic Solutions of an Elliptic Problem in Anisotropic Sobolev–Orlicz Spaces. J Math Sci 241, 258–284 (2019). https://doi.org/10.1007/s10958-019-04422-7
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DOI: https://doi.org/10.1007/s10958-019-04422-7
Keywords and phrases
- anisotropic elliptic equation
- entropic solution
- existence of solution
- Sobolev–Orlicz space
- N-function
- pseudo-monotonic operator