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.
|Original language||English (US)|
|Number of pages||20|
|Journal||SIAM Journal on Applied Mathematics|
|State||Published - Oct 1 2003|
- Fourth-order boundary value problems
- Progressive lens