How to prove existence in shape optimization
Dorin Bucur (2005)
Control and Cybernetics
Similarity:
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
Displaying similar documents to “Shape differentiability of the Neumann problem of the Laplace equation in the half-space”
How to prove existence in shape optimization
Weak shape formulation of free boundary problems
Jean-Paul Zolésio (1994)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Similarity:
On the ersatz material approximation in level-set methods
Marc Dambrine, Djalil Kateb (2010)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
The level set method has become widely used in shape optimization where it allows a popular implementation of the steepest descent method. Once coupled with a ersatz material approximation [Allaire , (2004) 363–393], a single mesh is only used leading to very efficient and cheap numerical schemes in optimization of structures. However, it has some limitations and cannot be applied in every situation. This work aims at exploring such a limitation. We estimate the systematic...
On solution to an optimal shape design problem in 3-dimensional linear magnetostatics
Dalibor Lukáš (2004)
Applications of Mathematics
Similarity:
In this paper we present theoretical, computational, and practical aspects concerning 3-dimensional shape optimization governed by linear magnetostatics. The state solution is approximated by the finite element method using Nédélec elements on tetrahedra. Concerning optimization, the shape controls the interface between the air and the ferromagnetic parts while the whole domain is fixed. We prove the existence of an optimal shape. Then we state a finite element approximation to the optimization...
An Elliptic Neumann Problem with Subcritical Nonlinearity
Jan Chabrowski, Kyril Tintarev (2005)
Bulletin of the Polish Academy of Sciences. Mathematics
Similarity:
We establish the existence of a solution to the Neumann problem in the half-space with a subcritical nonlinearity on the boundary. Solutions are obtained through the constrained minimization or minimax. The existence of solutions depends on the shape of a boundary coefficient.
Electrical Impedance Tomography: from topology to shape
Michael Hintermüller, Antoine Laurain (2008)
Control and Cybernetics
Similarity:
Indefinite Quasilinear Neumann Problem on Unbounded Domains
J. Chabrowski (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
Similarity:
We investigate the solvability of the quasilinear Neumann problem (1.1) with sub- and supercritical exponents in an unbounded domain Ω. Under some integrability conditions on the coefficients we establish embedding theorems of weighted Sobolev spaces into weighted Lebesgue spaces. This is used to obtain solutions through a global minimization of a variational functional.