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Based on truncation technique and priori estimates, we prove the existence and uniqueness of weak solution for a class of anisotropic nonlinear elliptic equations with variable exponent p(x)→ growth. Furthermore, we also obtain that the weak solution is locally bounded and regular; that is, the weak solution is Lloc∞(Ω) and C1,α(Ω).

On a Class of Anisotropic Nonlinear Elliptic Equations with Variable Exponent