TY  - BOOK
AU  - Bucur,Dorin
AU  - Buttazzo,Giuseppe
ED  - SpringerLink (Online service)
TI  - Variational Methods in Shape Optimization Problems
T2  - Progress in Nonlinear Differential Equations and Their Applications
SN  - 9780817644031
U1  - 515.64 23
PY  - 2005///
CY  - Boston, MA
PB  - Birkhäuser Boston
KW  - MATHEMATICS
KW  - FUNCTIONAL EQUATIONS
KW  - FUNCTIONAL ANALYSIS
KW  - DIFFERENTIAL EQUATIONS, PARTIAL
KW  - MATHEMATICAL OPTIMIZATION
KW  - CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION
KW  - OPTIMIZATION
KW  - PARTIAL DIFFERENTIAL EQUATIONS
KW  - DIFFERENCE AND FUNCTIONAL EQUATIONS
KW  - APPLICATIONS OF MATHEMATICS
N1  - to Shape Optimization Theory and Some Classical Problems -- Optimization Problems over Classes of Convex Domains -- Optimal Control Problems: A General Scheme -- Shape Optimization Problems with Dirichlet Condition on the Free Boundary -- Existence of Classical Solutions -- Optimization Problems for Functions of Eigenvalues -- Shape Optimization Problems with Neumann Condition on the Free Boundary
N2  - The study of shape optimization problems encompasses a wide spectrum of academic research with numerous applications to the real world. In this work these problems are treated from both the classical and modern perspectives and target a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems. Key topics and features: * Presents foundational introduction to shape optimization theory * Studies certain classical problems: the isoperimetric problem and the Newton problem involving the best aerodynamical shape, and optimization problems over classes of convex domains * Treats optimal control problems under a general scheme, giving a topological framework, a survey of "gamma"-convergence, and problems governed by ODE * Examines shape optimization problems with Dirichlet and Neumann conditions on the free boundary, along with the existence of classical solutions * Studies optimization problems for obstacles and eigenvalues of elliptic operators * Poses several open problems for further research * Substantial bibliography and index Driven by good examples and illustrations and requiring only a standard knowledge in the calculus of variations, differential equations, and functional analysis, the book can serve as a text for a graduate course in computational methods of optimal design and optimization, as well as an excellent reference for applied mathematicians addressing functional shape optimization problems
UR  - http://dx.doi.org/10.1007/b137163
ER  -