登入選單
返回Google圖書搜尋
Variational Methods in Shape Optimization Problems
Dorin BucurGiuseppe Buttazzo
出版Springer Science & Business Media, 2006-09-13
主題Mathematics / CalculusMathematics / AppliedMathematics / Differential Equations / GeneralMathematics / Functional AnalysisMathematics / Mathematical AnalysisMathematics / GeneralMathematics / Optimization
ISBN08176440329780817644031
URLhttp://books.google.com.hk/books?id=onwYsfhco2kC&hl=&source=gbs_api
EBookSAMPLE
註釋The fascinating ?eld of shape optimization problems has received a lot of attention in recent years, particularly in relation to a number of applications in physics and engineering that require a focus on shapes instead of parameters or functions. The goal of these applications is to deform and modify the admissible shapes in order to comply with a given cost function that needs to be optimized. In this respect the problems are both classical (as the isoperimetric problem and the Newton problem of the ideal aerodynamical shape show) and modern (re?ecting the many results obtained in the last few decades). The intriguing feature is that the competing objects are shapes, i.e., domains of N R , instead of functions, as it usually occurs in problems of the calculus of va- ations. This constraint often produces additional dif?culties that lead to a lack of existence of a solution and to the introduction of suitable relaxed formulations of the problem. However, in certain limited cases an optimal solution exists, due to the special form of the cost functional and to the geometrical restrictions on the class of competing domains.