Variational Methods in Shape Optimization Problems

  • Dorin Bucur
  • Giuseppe Buttazzo

Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 65)

About this book


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.


Excel functional analysis optimization ordinary differential equation partial differential equation

Authors and affiliations

  • Dorin Bucur
    • 1
  • Giuseppe Buttazzo
    • 2
  1. 1.Département de MathématiquesUniversité de MetzMetz Cedex 01France
  2. 2.Dipartimento di MatematicaUniversità di PisaPisaItaly

Bibliographic information