scholarly journals A new energy-gap cost functional approach for the exterior Bernoulli free boundary problem

2019 ◽  
Vol 8 (4) ◽  
pp. 785-824
Author(s):  
Julius Fergy T. Rabago ◽  
◽  
Hideyuki Azegami
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Energy Gap ◽  
Functional Approach ◽  
Cost Functional ◽  
New Energy ◽  
Bernoulli Free Boundary

Gamma limits in some Bernoulli free boundary problem

2005 ◽  
Vol 84 (1) ◽  
pp. 79-87 ◽  
Author(s):  
Bernd Kawohl ◽  
Henrik Shahgholian
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Bernoulli Free Boundary

scholarly journals On the supremal version of the Alt–Caffarelli minimization problem

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Graziano Crasta ◽  
Ilaria Fragalà
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Recent Work ◽  
Free Boundary Problem ◽  
Minimization Problem ◽  
Companion Paper ◽  
Infinity Laplacian ◽  
Link Type ◽  
Bernoulli Free Boundary

Abstract This is a companion paper to our recent work [Bernoulli free boundary problem for the infinity Laplacian, preprint 2018, https://arxiv.org/abs/1804.08573]. Here we consider its variational side, which corresponds to the supremal version of the Alt–Caffarelli minimization problem.

scholarly journals A free boundary problem for the Stokes equations

2016 ◽  
Vol 23 (1) ◽  
pp. 195-215 ◽  
Author(s):  
François Bouchon ◽  
Gunther H. Peichl ◽  
Mohamed Sayeh ◽  
Rachid Touzani
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Stokes Equations ◽  
Variational Problems ◽  
Shape Derivative ◽  
Cost Functional ◽  
A Free Boundary Problem ◽  
The Cost ◽  
Derivatives Of

A free boundary problem for the Stokes equations governing a viscous flow with over-determined condition on the free boundary is investigated. This free boundary problem is transformed into a shape optimization one which consists in minimizing a Kohn–Vogelius energy cost functional. Existence of the material derivatives of the states is proven and the corresponding variational problems are derived. Existence of the shape derivative of the cost functional is also proven and the analytic expression of the shape derivative is given in the Hadamard structure form.

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