On Numerically Implementable Explicit Formulas for the Solutions to the 2D and 3D Equations $\operatorname{div}(\alpha(w)\nabla w)=0$ and $\operatorname{div}(\beta\nabla w)=0$ with Cauchy Data on an Analytic Boundary

A construction of numerically implementable explicit expressions for the solutions of the two- and three-dimensional equations $\operatorname{div}(\alpha(w)\nabla w)=0$ and $\operatorname{div}(\beta\nabla w)=0$ with Cauchy data on an analytic boundary is presented.