Shape Optimization for Free Boundary Problems – Analysis and Numerics

2011 ◽  
pp. 277-288 ◽  
Author(s):  
Karsten Eppler ◽  
Helmut Harbrecht
Keyword(s):  
Free Boundary ◽  
Shape Optimization ◽  
Free Boundary Problems ◽  
Boundary Problems

scholarly journals On a numerical shape optimization approach for a class of free boundary problems

2020 ◽  
Vol 77 (2) ◽  
pp. 509-537
Author(s):  
A. Boulkhemair ◽  
A. Chakib ◽  
A. Nachaoui ◽  
A. A. Niftiyev ◽  
A. Sadik
Keyword(s):  
Free Boundary ◽  
Shape Optimization ◽  
Free Boundary Problems ◽  
Optimization Approach ◽  
Boundary Problems

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

2013 ◽  
Vol 58 (2) ◽  
pp. 205-221 ◽  
Author(s):  
Abdesslam Boulkhemair ◽  
Abdeljalil Nachaoui ◽  
Abdelkrim Chakib
Keyword(s):  
Free Boundary ◽  
Shape Optimization ◽  
Free Boundary Problems ◽  
Optimization Approach ◽  
Boundary Problems

scholarly journals A free boundary approach to shape optimization problems

2015 ◽  
Vol 373 (2050) ◽  
pp. 20140273 ◽  
Author(s):  
D. Bucur ◽  
B. Velichkov
Keyword(s):  
Free Boundary ◽  
Shape Optimization ◽  
Optimization Problem ◽  
Free Boundary Problems ◽  
Optimization Problems ◽  
General Shape ◽  
Dirichlet Laplacian ◽  
Boundary Problems ◽  
Survey Article ◽  
The Laplace Operator

The analysis of shape optimization problems involving the spectrum of the Laplace operator, such as isoperimetric inequalities, has known in recent years a series of interesting developments essentially as a consequence of the infusion of free boundary techniques. The main focus of this paper is to show how the analysis of a general shape optimization problem of spectral type can be reduced to the analysis of particular free boundary problems. In this survey article, we give an overview of some very recent technical tools, the so-called shape sub- and supersolutions, and show how to use them for the minimization of spectral functionals involving the eigenvalues of the Dirichlet Laplacian, under a volume constraint.

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