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 $L_1$ and prove the existence of entropic solutions in anisotropic Sobolev–Orlicz
spaces.
Keywords:anisotropic elliptic equation, entropic solution, existence of
solution, Sobolev–Orlicz space, $N$-function, pseudo-monotonic operator.
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