Analysis of a variational approach to progressive lens design

Jing Wang, Robert Gulliver, Fadil Santosa

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


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 languageEnglish (US)
Pages (from-to)277-296
Number of pages20
JournalSIAM Journal on Applied Mathematics
Issue number1
StatePublished - Oct 2003


  • Fourth-order boundary value problems
  • Progressive lens
  • Well-posedness


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