Hausdorff convergence of domains and their boundaries for shape optimal design

• Autorzy: Holzleitner L.
• Języki publikacji: EN

Abstrakty

EN

A question, which arises frequently in shape optimal design, is the convergence of domains. If the objective function is defined by using the solution of a PDE with boundary conditions, then also the convergence of the boundary is of importance. In this paper a criterion for a set of domains is defined, such that from [Omega_n] --> Omega follows [Gamma_n] --> Gamma if one is restricting to this set of domains. Moreover it is proved that this criterion is sharp, meaning that if [Omega_n] --> Omega implies [Gamma_n] --> Gamma holds for any sequence of this set, then this criterion has to be fulfilled. A similar criterion for the convergence of the Lebesgue measure of the boundaries my(Gamma_n) --> my(Gamma) is given.

Słowa kluczowe

EN

Hausdorff convergence; Hausdorff metric; hyperspace; shape optimization

PL

hiperprzestrzeń; konwergencja Hausdorffa; miara Haudorffa

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2001
• Tom: Vol. 30, no 1
• Strony: 23--44
• Opis fizyczny: Bibliogr. 19 poz.,

Twórcy

autor

Holzleitner L.