Journal of Evolution Equations

, Volume 10, Issue 3, pp 551–570

Second-order domain derivative of normal-dependent boundary integrals


DOI: 10.1007/s00028-010-0061-3

Cite this article as:
Balzer, J. J. Evol. Equ. (2010) 10: 551. doi:10.1007/s00028-010-0061-3


Numerous reconstruction tasks in (optical) surface metrology allow for a variational formulation. The occurring boundary integrals may be interpreted as shape functions. The paper is concerned with the second-order analysis of such functions. Shape Hessians of boundary integrals are considered difficult to find analytically because they correspond to third-order derivatives of an, in a sense equivalent, domain integral. We complement previous results by considering cost functions depending explicitly on the surface normal. The correctness and practicability of our calculations are verified in the context of a Newton-type shape reconstruction method.

Mathematics Subject Classification (2000)

49Q10 49Q12 


Shape optimization Domain derivative Shape Hessian Generalized Newton method Boundary integral Shape evolution Level set method Reconstruction 

Copyright information

© Birkhäuser / Springer Basel AG 2010

Authors and Affiliations

  1. 1.Geometric Modeling and Scientific Visualization CenterKing Abdullah University of Science and TechnologyThuwalKingdom of Saudi Arabia