# A shape optimization approach for a class of free boundary problems of Bernoulli type

Abdesslam Boulkhemair; Abdeljalil Nachaoui; Abdelkrim Chakib

Applications of Mathematics (2013)

- Volume: 58, Issue: 2, page 205-221
- ISSN: 0862-7940

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topBoulkhemair, Abdesslam, Nachaoui, Abdeljalil, and Chakib, Abdelkrim. "A shape optimization approach for a class of free boundary problems of Bernoulli type." Applications of Mathematics 58.2 (2013): 205-221. <http://eudml.org/doc/252510>.

@article{Boulkhemair2013,

abstract = {We are interested in an optimal shape design formulation for a class of free boundary problems of Bernoulli type. We show the existence of the optimal solution of this problem by proving continuity of the solution of the state problem with respect to the domain. The main tools in establishing such a continuity are a result concerning uniform continuity of the trace operator with respect to the domain and a recent result on the uniform Poincaré inequality for variable domains.},

author = {Boulkhemair, Abdesslam, Nachaoui, Abdeljalil, Chakib, Abdelkrim},

journal = {Applications of Mathematics},

keywords = {shape optimization; Bernoulli; free boundary problem; exterior Bernoulli problem; optimal solution; state problem; continuity of the state problem; uniform tubular neighbourhood; diffeomorphism; uniform trace theorem; uniform Poincaré inequality; shape optimization; free boundary problem; exterior Bernoulli problem; optimal solution; state problem; uniform tubular neighbourhood; diffeomorphism; uniform trace theorem; uniform Poincaré inequality},

language = {eng},

number = {2},

pages = {205-221},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {A shape optimization approach for a class of free boundary problems of Bernoulli type},

url = {http://eudml.org/doc/252510},

volume = {58},

year = {2013},

}

TY - JOUR

AU - Boulkhemair, Abdesslam

AU - Nachaoui, Abdeljalil

AU - Chakib, Abdelkrim

TI - A shape optimization approach for a class of free boundary problems of Bernoulli type

JO - Applications of Mathematics

PY - 2013

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 58

IS - 2

SP - 205

EP - 221

AB - We are interested in an optimal shape design formulation for a class of free boundary problems of Bernoulli type. We show the existence of the optimal solution of this problem by proving continuity of the solution of the state problem with respect to the domain. The main tools in establishing such a continuity are a result concerning uniform continuity of the trace operator with respect to the domain and a recent result on the uniform Poincaré inequality for variable domains.

LA - eng

KW - shape optimization; Bernoulli; free boundary problem; exterior Bernoulli problem; optimal solution; state problem; continuity of the state problem; uniform tubular neighbourhood; diffeomorphism; uniform trace theorem; uniform Poincaré inequality; shape optimization; free boundary problem; exterior Bernoulli problem; optimal solution; state problem; uniform tubular neighbourhood; diffeomorphism; uniform trace theorem; uniform Poincaré inequality

UR - http://eudml.org/doc/252510

ER -

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