# On the normal variations of a domain

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 3, page 251-261
- ISSN: 1292-8119

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topBresch, D., and Simon, J.. "On the normal variations of a domain ." ESAIM: Control, Optimisation and Calculus of Variations 3 (2010): 251-261. <http://eudml.org/doc/197339>.

@article{Bresch2010,

abstract = {
In domain optimization problems, normal variations of a reference domain are frequently used. We prove that such variations do not
preserve the regularity of the domain. More precisely, we give a bounded domain which boundary is m times differentiable and a
scalar variation which is infinitely differentiable such that the deformed boundary is only m-1 times differentiable. We prove in
addition that the only normal variations which preserve the regularity are those with constant magnitude.
This shows that the use of normal variations in an iterative approximation method for domain optimization generates a loss of
regularity at each iteration, and thus it is better to use transverse variations which preserve the regularity of the domain.
},

author = {Bresch, D., Simon, J.},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Domain variations; optimal design; boundary differentiability. ; boundary differentiability; domain optimization; normal variations; regularity; transverse variations},

language = {eng},

month = {3},

pages = {251-261},

publisher = {EDP Sciences},

title = {On the normal variations of a domain },

url = {http://eudml.org/doc/197339},

volume = {3},

year = {2010},

}

TY - JOUR

AU - Bresch, D.

AU - Simon, J.

TI - On the normal variations of a domain

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 3

SP - 251

EP - 261

AB -
In domain optimization problems, normal variations of a reference domain are frequently used. We prove that such variations do not
preserve the regularity of the domain. More precisely, we give a bounded domain which boundary is m times differentiable and a
scalar variation which is infinitely differentiable such that the deformed boundary is only m-1 times differentiable. We prove in
addition that the only normal variations which preserve the regularity are those with constant magnitude.
This shows that the use of normal variations in an iterative approximation method for domain optimization generates a loss of
regularity at each iteration, and thus it is better to use transverse variations which preserve the regularity of the domain.

LA - eng

KW - Domain variations; optimal design; boundary differentiability. ; boundary differentiability; domain optimization; normal variations; regularity; transverse variations

UR - http://eudml.org/doc/197339

ER -

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