Numerical computation of least constants for the Sobolev inequality
Numerische Mathematik
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Exact and Approximate Controllability for Distributed Parameter Systems: A Numerical Approach (Encyclopedia of Mathematics and its Applications)
Solving a non-smooth eigenvalue problem using operator-splitting methods
International Journal of Computer Mathematics - Splitting Methods for Differential Equations
Non-smooth SOR for L1-Fitting: Convergence Study and Discussion of Related Issues
Journal of Scientific Computing
Introduction to Derivative-Free Optimization
Introduction to Derivative-Free Optimization
Numerical Methods for the Vector-Valued Solutions of Non-smooth Eigenvalue Problems
Journal of Scientific Computing
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A numerical method for the computation of the best constant in a Sobolev inequality involving the spaces H 2(驴) and $C^{0}(\overline{\Omega})$ is presented. Green's functions corresponding to the solution of Poisson problems are used to express the solution. This (kind of) non-smooth eigenvalue problem is then formulated as a constrained optimization problem and solved with two different strategies: an augmented Lagrangian method, together with finite element approximations, and a Green's functions based approach. Numerical experiments show the ability of the methods in computing this best constant for various two-dimensional domains, and the remarkable convergence properties of the augmented Lagrangian based iterative method.