Analysis of a Variational Approach to Progressive Lens Design

Abstract

We consider a variational approach to the progressive lens design problem. The corresponding Euler--Lagrange equation is a fourth-order nonlinear elliptic partial differential equation. We analyze two linearizations of the equation and show the existence and uniqueness as well as the regularity of the solutions for various boundary conditions. We end with an example of a progressive lens designed by solving the elliptic partial differential equation.