Trial Methods for Nonlinear Bernoulli Problem

1997 ◽  
pp. 260-267
Author(s):  
Kari Kärkkäinen ◽  
Timo Tiihonen
Keyword(s):  
Bernoulli Problem

The Bernoulli Problem

1987 ◽  
pp. 5-33 ◽  
Author(s):  
Sergei M. Rytov ◽  
Yurii A. Kravtsov ◽  
Valeryan I. Tatarskii
Keyword(s):  
Bernoulli Problem

scholarly journals A Dirichlet–Neumann cost functional approach for the Bernoulli problem

2013 ◽  
Vol 81 (1) ◽  
pp. 157-176 ◽  
Author(s):  
A. Ben Abda ◽  
F. Bouchon ◽  
G. H. Peichl ◽  
M. Sayeh ◽  
R. Touzani
Keyword(s):  
Functional Approach ◽  
Cost Functional ◽  
Bernoulli Problem

The nonstationary Bernoulli problem with fixed boundary

1999 ◽  
Vol 73 (1) ◽  
pp. 56-63
Author(s):  
Alfred Wagner
Keyword(s):  
Fixed Boundary ◽  
Bernoulli Problem

scholarly journals Stabilization of the trial method for the Bernoulli problem in case of prescribed Dirichlet data

2014 ◽  
Vol 38 (13) ◽  
pp. 2850-2863 ◽  
Author(s):  
Helmut Harbrecht ◽  
Giannoula Mitrou
Keyword(s):  
Dirichlet Data ◽  
Bernoulli Problem

scholarly journals Regularity of the free boundary for the two-phase Bernoulli problem

2021 ◽  
Author(s):  
Guido De Philippis ◽  
Luca Spolaor ◽  
Bozhidar Velichkov
Keyword(s):  
Free Boundary ◽  
Optimization Problem ◽  
Principal Eigenvalue ◽  
Dirichlet Laplacian ◽  
Regularity Theorem ◽  
Two Phase ◽  
Regularity Of Minimizers ◽  
Spectral Optimization ◽  
Bernoulli Problem

AbstractWe prove a regularity theorem for the free boundary of minimizers of the two-phase Bernoulli problem, completing the analysis started by Alt, Caffarelli and Friedman in the 80s. As a consequence, we also show regularity of minimizers of the multiphase spectral optimization problem for the principal eigenvalue of the Dirichlet Laplacian.

scholarly journals Bernoulli problem for rough domains

2015 ◽  
Vol 22 (2) ◽  
pp. 131-146
Author(s):  
François Bouchon ◽  
Laurent Chupin
Keyword(s):  
Bernoulli Problem

scholarly journals On the First-Order Shape Derivative of the Kohn-Vogelius Cost Functional of the Bernoulli Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-19 ◽  
Author(s):  
Jerico B. Bacani ◽  
Gunther Peichl
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Optimization Techniques ◽  
Shape Derivative ◽  
State Variables ◽  
Cost Functional ◽  
First Order ◽  
Bernoulli Problem ◽  
The Cost

The exterior Bernoulli free boundary problem is being considered. The solution to the problem is studied via shape optimization techniques. The goal is to determine a domain having a specific regularity that gives a minimum value for the Kohn-Vogelius-type cost functional while simultaneously solving two PDE constraints: a pure Dirichlet boundary value problem and a Neumann boundary value problem. This paper focuses on the rigorous computation of the first-order shape derivative of the cost functional using the Hölder continuity of the state variables and not the usual approach which uses the shape derivatives of states.

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