The Dirichlet problem in arbitrary domains for a wide class of anisotropic elliptic equations of the second order with variable exponent nonlinearities and the right-hand side as a measure is considered. The existence of an entropy solution in anisotropic Sobolev spaces with variable exponents is established.It is proved that the obtained entropy solution is a renormalized solution of the considered problem.
On solutions of elliptic equations with variable exponents and measure data in $\mathbb{R}^n$
On a scale of anisotropic Sobolev spaces
Homogenization of the boundary value for the Dirichlet Problem
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