Frontiers of Mathematics in China >
Existence and uniqueness for variational problem from progressive lens design
Received date: 12 Mar 2020
Accepted date: 16 Jun 2020
Published date: 15 Jun 2020
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We study a functional modelling the progressive lens design, which is a combination of Willmore functional and total Gauss curvature. First, we prove the existence for the minimizers of this class of functionals among the class of revolution surfaces rotated by the curves y = f(x) about the x-axis. Then, choosing such a minimiser as background surfaces to approximate the functional by a quadratic functional, we prove the existence and uniqueness of the solution to the Euler-Lagrange equation for the quadratic functionals. Our results not only provide a strictly mathematical proof for numerical methods, but also give a more reasonable and more extensive choice for the background surfaces.
Huaiyu JIAN , Hongbo ZENG . Existence and uniqueness for variational problem from progressive lens design[J]. Frontiers of Mathematics in China, 2020 , 15(3) : 491 -505 . DOI: 10.1007/s11464-020-0845-x
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