We study the anisotropic boundary value problem <img border=0 width=344 height=62 src="http://fbpe/img/cubo/v12n1/art12-01.jpg">on <img border=0 width=18 height=21 src="http://fbpe/img/cubo/v12n1/img30.jpg"><img border=0 width=20 height=22 src="http://fbpe/img/cubo/v12n1/img11.jpg">, where <img border=0 width=20 height=22 src="http://fbpe/img/cubo/v12n1/img11.jpg">is a smooth open bounded domain in <img border=0 width=238 height=29 src="http://fbpe/img/cubo/v12n1/art12-02.jpg">. We prove the existence and uniqueness of an entropy solution for this problem.