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
AV  - QA315-316 
U1  - 515.64 23
PY  - 2005///
CY  - Boston, MA
PB  - Birkh�user Boston
KW  - Mathematics
KW  - Difference equations
KW  - Functional equations
KW  - Functional analysis
KW  - Partial differential equations
KW  - Applied mathematics
KW  - Engineering mathematics
KW  - Mathematical optimization
KW  - Calculus of variations
KW  - Calculus of Variations and Optimal Control; Optimization
KW  - Optimization
KW  - Partial Differential Equations
KW  - Functional Analysis
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  -