On a Shape Derivative Formula with Respect to Convex Domains

被引：0

作者：

Boulkhemair, A. ^{[1
]}

Chakib, A. ^{[2
]}

机构：

[1] Univ Nantes, CNRS, Lab Mathemat Jean Leray, UMR6629, F-44322 Nantes, France

[2] Univ Sultan Moulay Slimane, FST Beni Mellal, Lab Mathemat & Applicat, Beni Mellal, Morocco

来源：

JOURNAL OF CONVEX ANALYSIS | 2014年 / 21卷 / 01期

关键词：

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We extend to the case of W-loc(1,1) functions a formula, known for C-1 functions, for the computation of the shape derivative of an integral cost functional with respect to a class of admissible convex domains. The convexity context allows one to use the support functions of the domains to express the shape derivative. We shall also illustrate the formula by applying it to the computation of the shape derivative for a shape optimization problem and by giving an algorithm.

引用

页码：67 / 87

页数：21

共 50 条

[1] On a Shape Derivative Formula with Respect to Convex Domains (vol 21, pg 67, 2014)
Boulkhemair, A.
Chakib, A.
JOURNAL OF CONVEX ANALYSIS, 2015, 22 (03) : 901 - 903
[2] Frechet derivative with respect to the shape of a strongly convex nonscattering region in optical tomography
Hyvoenen, Nuutti
INVERSE PROBLEMS, 2007, 23 (05) : 2249 - 2270
[3] On a shape derivative formula for star-shaped domains using Minkowski deformation
Boulkhemair, Abdesslam
Chakib, Abdelkrim
Sadik, Azeddine
AIMS MATHEMATICS, 2022, 8 (08): : 19773 - 19793
[4] On transfinite interpolations with respect to convex domains
Randrianarivony, Maharavo
COMPUTER AIDED GEOMETRIC DESIGN, 2011, 28 (02) : 135 - 149
[5] Eigenpair derivative with respect to boundary shape
Liu, ZS
Hu, HC
AIAA JOURNAL, 1997, 35 (01) : 167 - 171
[6] THE LINDELOF PRINCIPLE AND THE ANGULAR DERIVATIVE IN STRONGLY CONVEX DOMAINS
ABATE, M
JOURNAL D ANALYSE MATHEMATIQUE, 1990, 54 : 189 - 228
[7] STABILIZABILITY OF STRICT CONVEX PROCESSES WITH RESPECT TO ARBITRARY STABILITY DOMAINS
Oner, Isil
Camlibel, M. Kanat
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2023, 61 (03) : 1819 - 1834
[8] ON A SHAPE DERIVATIVE FORMULA IN THE BRUNN-MINKOWSKI THEORY
Boulkhemair, A.
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2017, 55 (01) : 156 - 171
[9] Sharp estimates for partial derivative on convex domains of finite type
Cumenge, A
ARKIV FOR MATEMATIK, 2001, 39 (01): : 1 - 25
[10] Compactness of the partial derivative-Neumann problem on convex domains
Fu, SQ
Straube, EJ
JOURNAL OF FUNCTIONAL ANALYSIS, 1998, 159 (02) : 629 - 641

← 1 2 3 4 5 →