scholarly journals On a variational principle for shape optimization and elliptic free boundary problems

2009 ◽  
Vol 6 (1) ◽  
pp. 67
Author(s):  
Raúl B. González De Paz
Keyword(s):  
Variational Principle ◽  
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.

Solvability of free boundary problems for steady groundwater flow

2015 ◽  
Vol 26 (6) ◽  
pp. 821-847 ◽  
Author(s):  
A. Yu. BELIAEV
Keyword(s):  
Variational Principle ◽  
Free Boundary ◽  
Weak Solutions ◽  
Input Data ◽  
Free Boundary Problems ◽  
Boundary Problems ◽  
Phreatic Surface ◽  
Existence Of Weak Solutions ◽  
Lower Semi ◽  
Flow Domain

In this paper the free boundary problem for groundwater phreatic surface is represented in the form of a variational principle. It is proved that the flow domain Ω that solves the problem is a minimizer of some functional Λ(Ω). Weak solutions are introduced as minimizers of the lower semi-continuous regularization of Λ(⋅). Within this approach the existence of weak solutions is proved for a wide class of input data.

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